"Mathematics / Statistics" Essays

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Decision to Become a Math Research Paper

Research Paper  |  2 pages (625 words)
Bibliography Sources: 2


Math majors seeking a career in this field will be rewarded by high salaries ($42.14 per hour median), faster than average job growth (27%), and a non-competitive job market ("Actuaries: Summary" 2012). In addition, a bachelor's degree is usually sufficient for obtaining an actuary position, although certification is generally required.

For math majors interested in research, but uncertain about pursuing a graduate degree, there are a few opportunities available. Biostatistics is a discipline barely more than a decade old, but the need is great for mathematicians interested in applying their talents and skills to problems in basic biology research, medicine, and public health (epidemiology). Biologists and biomedical researchers have advanced to the point where they have too much data and not enough knowledge about statistics and math (Kling 2004). Although math majors have been taking biology courses and entering the biostatistics profession, the need remains great. The ideal biostatistician would be well-versed in biology, applied mathematics, statistics, bioinformatics, and computer programming. While a bachelor's degree was at one time sufficient, the field is growing and maturing so fast that graduate degrees are becoming more common. While most job opportunities for biostatisticians exist in academia, the pharmaceutical industry expects biostatisticians to represent the fastest growing segment.


"Actuaries: Summary." Bureau of Labor Statistics, U.S. Department of Labor. Last modified April 5, 2012. http://www.bls.gov/ooh/math/actuaries.htm.

Kling, Jim. "The mathematical biology job market." Science Careers. Published 27 Feb. 2004. http://sciencecareers.sciencemag.org/career_magazine/previous_issues/articles/2004_02_27/noDOI.6305720559640560046.

"Mathematicians: How to become a mathematician." Bureau of Labor Statistics, U.S. Department of Labor. Last modified March 29, 2012. http://www.bls.gov/ooh/math/mathematicians.htm#tab-4.

"Mathematicians: Summary." Bureau of Labor Statistics, U.S. Department of Labor. Last modified March 29, 2012. http://www.bls.gov/ooh/math/mathematicians.htm.

"Statisticians: Summary." Bureau of Labor Statistics, U.S. Department of Labor. Last modified June 26, 2012. http://www.bls.gov/ooh/math/statisticians.htm.… [read more]

Statistics in Research and Analysis the Experiments Research Paper

Research Paper  |  10 pages (3,309 words)
Bibliography Sources: 10


¶ … Statistics in Research and Analysis

The experiments, analysis and statistics-5

Uses of statistics in experiments and research-5

Tools of Analysis-7

Experimental Design-9

Common uses in every day life-12


This paper concerns itself with the use of statistics as a means and the important tool in research and analysis -- both in… [read more]

Art and Mathematics Are Related Research Paper

Research Paper  |  10 pages (2,688 words)
Bibliography Sources: 1+


¶ … art and mathematics are related and that this relation could be used to the advantage of educators to overcome student anxiety regarding mathematics and, in particular, difficult geometry concepts

Outline the basic topics to be covered in the study

What is hyperbolic geometry?

Who is MC Escher?

How does Escher's work relate to hyperbolic geometry?

How to design… [read more]

Mathematics in Digital Photography Research Paper

Research Paper  |  3 pages (925 words)
Bibliography Sources: 3


Compression technology is the primary driver behind the vast expansion of digital photography. Compression allows large amounts of data to be stored in a relatively small area so that more intricate details of the photo can be accurately reconstructed.

Compression is a complicated process that involves several steps. The first step is to convert red, green, and blue color channels to Y, Cb, and Cr channels while partitioning blocks into size 8x8 pixels. For a JPEG image, the compression relies on the Discrete Cosine Transformation, which is exemplified by the equation: C = UBU^T, where B. is one of the 8x8 blocks and U. is a special 8x8 matrix. Applying certain methods of encoding enables compression of about 70% in most instances, or even more in some circumstances. The process can then be inverted to expand the image and view it in full, by finding B. For the previous equation:

B^' = U^T C^'U for each block ("Image Compression," 2011).

One downside of this compression technique for JPEG images is that decoupling can occur causing some parts of the image to appear blocky. While this loss of resolution is often within the range of acceptability, sometimes it is not good enough for certain publications, such as magazines or other media ("Image Compression," 2011). It is possible that the compression algorithms will continue to improve as both the mathematical concepts and computing power rendering them continue to improve.


There are many different applications of mathematics when it comes to digital photography. The equations are used for everything from the mathematical rendering of color to the compression of files down to a size that is easily stored and converted back to much more intricate images. The advances in both cameras and the software that helps to edit and alter the images have allowed many people to take pictures with their cell phones that would have required much more expensive cameras just a few short years ago. The realm of the professional photographer has been entered by every person sitting at home with a digital camera and a suite of photo editing programs, such as Adobe. Furthermore, the compression of the photos has allowed them to be easily shared over the Internet and between friends on their cell phones or Facebook pages. This marks a huge turning point in modern photography and one that will doubtless continue to push the boundaries of what is possible with digital cameras.


Higham, N. (2007). The mathematics of digital photography. Retrieved from:


Hoggar, S.G. (2006). Mathematics of digital images. Cambridge, UK: Cambridge

Image Compression: How Math Led to the JPEG2000 Standard. (2011). Society for Industrial

And Applied Mathematics. Retrieved from:

http://www.whydomath.org/node/wavlets/basicjpg.html.… [read more]

Statistics Are Integral to Research Term Paper

Term Paper  |  2 pages (713 words)
Bibliography Sources: 0


Statistics are integral to research but it is important to know how to read, interpret, and use statistics so that one can best comprehend what one is reading and not be duped by those who may distort statistical data for subjective purposes.

Statistics are powerful, but used incorrectly or erroneously they can also distort information and lead to negative results. Just as words are ambiguous, numbers and images (such as tables, flowcharts, graphs etc.) can be misleading too.

Reading articles that contain statistical data involves a critical manner throughout and involves practicing critical techniques.

Firstly, one has to constantly question the source of the data. Even when extracted from a scientific article, the journal needs to be checked to see whether it is a peer-reviewed credible source. This refers all the more so for popular books and articles. All too often, people assume diets and do-it-yourself treatments that can be potentially destructive at their worst due to respect for statistics and the fact that the data was extracted from a journal or book that contained 'psychology' or 'science' as its tile. The background of the author has to be carefully reviewed, as well as the publisher, and the context of the statistics.

The presented data may indicate only a part of the picture. Questions, therefore, have to be asked, as for instance: the purpose of the data, the subjectivity of the researcher, the intention of his research, the policy or procedure that hinges on the statistics, and so forth. Illustrative of this fact are statistics that convey some political process, as for instance, the current Iraqi conflict. A good number of the sources are partisan, and the statistical data, authoritative and impressive as they seem, too readily reflect the interest of one side or the other.

Related to this is the investigation to discover whether all the data has been included. To return to the Iraqi conflict scenario again, some data may have been intentionally excluded or presented in an incongruous manner. The other side of the picture -- and the entire picture -- has to be seen for an accurate perspective to be garnered.

Statistics…… [read more]

NCTM's Agenda for Action and Standards Term Paper

Term Paper  |  2 pages (517 words)
Bibliography Sources: 1



Over time, new generations of students come equipped with unique and different background knowledge. In the 1980s, NCTM, or the National Council of Teachers of Mathematics, launched a new Agenda for Action. American students had moved from a largely agricultural-based society to one that was focused on science, technology, and information. NCTM provides the blueprints from which mathematic curriculum is built across the country. In order to meet the needs of a changing society, they felt the urgent need to update the mathematic standards to fit the students of the 80s, and they continue to update the standards for today's students (Krulic, 2003, p. 21).

Many updates were made to the Agenda for Action in 2000. In the 1989 version, four standards, called process standards, were presented and reached across all grade levels, k-12: problem solving, communications, reasoning, and connections. When updated in 2000, the fifth standard of representation was added. This new process standard suggested that students now learn in reasoning skills, strategies for solving problems, understand relationships between different types of mathematics, as well as the relationships between mathematics and the other disciplines (Krulic, 2003, p. 22). Several changes were made. Communication skills, which had been long overlooked when teaching mathematics, was now being emphasized through writing, listening, and other communication about math (Krulic, 2003, p. 22-23). Connections were also being focused on, looking at the mathematical discipline as a single unit rather than numerous smaller individual parts (Krulic, 2003, p. 23). The process standards suggested a large shift in grade placement and content levels…… [read more]

SPSS Statistics: Social Science Research Instructions: Reading Essay

Essay  |  2 pages (473 words)
Bibliography Sources: 1


SPSS Statistics: Social Science Research


Reading: Chapter 11-14 - SPSS Statistics 17.0 - Guide to Data Analysis by Marija J. Norusis

Other attachments to follow.

Use Assignment 7a -- Tutorial

Problem 7 ?" Chapter 12:

Use the select cases facility to select only men with coronary heart disease ( variable chd equals 1). Test the hypothesis that they come from a population in which the average serum cholesterol is 205 mg/dl (variable chol58).

State the null and alternative hypotheses.

Ho: The population mean is not equal to 205.

Ha: The population mean is equal to 205.

What so you conclude about the null hypothesis based on the t test?

The null hypothesis is supported. The sample mean is significantly different from a mean of 205.

What is the difference between your sample mean and the hypothetical population value?


d. How often would you expect to see a sample difference at least this large in absolute value if the null hypothesis is true?

e. Give range of values that you are 95% confident include the population value for the mean cholesterol of men with coronary heart disease. Does the interval include your test value of 205?

257.66 to 278.98. This does not include the test value of 205.

Assignment #7b:

Use Assignment 7b -- Tutorial

Problem 9 ?" Chapter 12:

The leader of the Chicago schools claims that dramatic improvements have occurred between 1993 and…… [read more]

Actuaries the Jobs Rated Almanac Term Paper

Term Paper  |  2 pages (741 words)
Style: APA  |  Bibliography Sources: 4


The career itself requires a solid understanding of mathematics in order to analyze statistics, make recommendations and generalizations based on those statistics, monitor the financial situation of the companies they work for, and provide consultation on investment strategies (Society of Actuaries, n.d.). They also use statistical analysis to infer the probability of an undesirable event from occurring, and the likely cost related to such an event. Furthermore, they address many financial questions such as how much money should one contribute to a pension plan and how often to produce a certain retirement income level by a specified time. Finally, actuaries use their statistical, financial, and business knowledge to help design savings plans, pension plans, insurance policies, and other financial programs to help protect people and their assets from potential risks.

Actuaries are highly valued individuals (Society of Actuaries, n.d.). Their expertise is needed by society to ensure that we are protected from many of life's undesirable events. Their creativity and knowledge creates strategies to prevent such events from occurring, which relieves us of emotional pain and financial burden. Undesirable events which do occur do not have as strong of an impact on us as because of the work they do. "Actuaries…are the brains behind the financial safeguards we have implemented in our personal lives, so we can go about our daily lives without worrying too much about what the future may hold for us" (Society of Actuaries, n.d.). Furthermore, it is the knowledge that actuaries' posses regarding risks and risk-reduction which have informed many of the savings programs we invest into. These programs allow us to protect ourselves and enjoy many of life's pleasures. Thus, we all benefit from the work of actuaries.


Braverman, B. & Jeffries, A. (2009, December 1). Top-paying jobs. CNNMoney.com. Retrieved from http://finance.yahoo.com/personal-finance/article/108264/top-paying-jobs.

Department of Mathematics. (n.d.). Actuarial studies. University of Texas at Austin.

Retrieved from: http://www.ma.utexas.edu/dev/actuarial.

Kouba, D. (n.d.). Why choose a mathematics-related profession? University of California.

Retrieved from: http://www.math.ucdavis.edu/~kouba/MathJobs.html.

Society of Actuaries & Casualty Actuarial Society. (n.d.). Be an Actuary. Retrieved from:

www.beanactuary.org.… [read more]

Statistics: Marketing the Practice Applying One's Knowledge Essay

Essay  |  2 pages (534 words)
Style: APA  |  Bibliography Sources: 2


Statistics: Marketing the Practice

Applying one's knowledge and skills in statistics and statistical applications is not too difficult, especially when the client or end user is concerned about the validity or reliability (or both) of the data. However, as with other practice of experts in a particular field or area of expertise, the challenge to promoting the use of statistics is on the manner by which practitioners (i.e., statisticians) "market" this discipline and their expertise.

The science of statistics make this field an especially exclusive niche for academicians, and at most, practitioners working as "specialists" for statistics-dependent industries, such as market/business research and management consulting industries. Statisticians working for the academe and specialist industries have different approaches to implementing statistics in their respective fields. Statisticians working for the academe implement statistical principles, techniques, and applications with great rigor, and they usually work on projects that look at issues or problems from a generalist's approach. That is, statistics as applied in checking for data quality and analyses in the academe caters specifically to the project itself, with a broader look at how the project's findings will be used as a becnhmark or standard to similar kinds of studies.

Statisticians working as specialists for a specific industry, meanwhile, would have a more specific approach to applying statistics in their chosen field of expertise. Statisticians working for market research agencies or consulting firms would apply statistical techniques and principles to answer a client's business needs and issues, and each project's findings will betreated as confidential and would not be integrated for public use. Instead, this compilation of studies would be…… [read more]

Statistics in Management Essay

Essay  |  3 pages (781 words)
Bibliography Sources: 3


Statistics in Management: Descriptive vs. Inferential Statistics

The use of descriptive vs. inferential statistics in organizations provides decision makers, managers and leaders with the necessary insights to compete more effectively in an increasingly challenging global economic climate. The intent of this essay is to define which conditions are optimal for the use of each. Descriptive statistics by definition are more adept at the consolidating of data and its summarization (Spatz, 2008). Inferential statistics however are meant to be representative of a broader population and are developed to be statistically sound (van den Besselaar, 2003). The use of each of these types of statistics varies significantly within organizations, and has completely different interpretations when used. This essay examines how each are used to their optimal value.

Best Practices in Descriptive Statistics

There are several functional areas within organizations that rely heavily on descriptive statistics. These include accounting, business planning and analysis, financial planning, marketing, sales, product management, quality and production. Each of these functional areas are often evaluated on scorecards and benchmarks-based entirely on descriptive statistics of their activity over time (Ainslie, Leyland, 1992). Best practices in descriptive statistics for example in marketing centers on the need to accurately and succinctly summarize customer feedback about existing marketing strategies, experiences with customer service centers, and the prices paid for products as well. Descriptive statistics is an indispensible tool for evaluating which strategies are best used for retaining and growing customer loyalty as well (Ainslie, Leyland, 1992). In the area of production, descriptive statistics are very useful for evaluating the effectiveness of production techniques, systems and routing of specific products over the shop floor. This is exceptionally valuable for getting greater performance and production from less space, as lean manufacturing techniques rely on descriptive statistics for insights into how to continually improve. As these examples within organizations indicate, descriptive statistics are best for creating a synopsis or summary of a given set of variables that have a major impact on the organization. From customers to suppliers and production processes, descriptive statistics are invaluable for gaining insights into how to improve an organization over time.

Inferential Statistics and the Defining of Strategies in Organizations

The conditions for applying inferential statistics in an organization are when the data has been statistically and reliably collected to reflect a broader population of users. Inferential statistics are best…… [read more]

Impact of Mathematics on Economics From the Medieval Time Thesis

Thesis  |  1 pages (377 words)
Style: APA  |  Bibliography Sources: 2


¶ … mathematics on economics: Medieval era

A number of new developments occurred during the early Middle Ages in the Arab world to make current methods of calculating economic principles possible: the first was the development of so-called 'Arabic' numbers, which enabled easier calculation methods than the numbers of the Roman numerical system, and the second major influence was that of the development of algebra. However, in Europe, in stark contrast to the ancient Romans and Greeks as well as their Arab contemporaries, medieval Europeans during the feudal era seemed to have less of a fascination with exact calculations and geometric theories. "The Church's education program consisted of schools which taught what was dictated by the Bible and the Pope, they were attached to churches, operated by monks and taught from the geometric, musical, and arithmetic compilations of Anicius Manlius Severinus Boethius" (Dickerson 1996). Theology rather than mathematics was the most celebrated of all the intellectual disciplines.

Only with the expansion of capitalism did things begin to change. The increased use of money as a placeholder of value, the evolution more elaborate government bureaucracies and national taxation systems…… [read more]

Damned Lies and Statistics by Joel Best Research Proposal

Research Proposal  |  1 pages (409 words)
Style: MLA  |  Bibliography Sources: 1


¶ … Damned Lies and Statistics by Joel Best discusses both the uses and misuses of statistics, particularly in relation to social issues, problems, changes, and policies. Best puts his focus especially on the use of social statistics as issues and problems because information received and beliefs and perceptions developed from social statistics have a beneficial and detrimental effect to the lives of people in a society.

In his book, Best surveyed current literature, both popular and scientific/technical, that uses social statistics as bases for their claims and arguments. He noted that more often than not, this growing body of literature that is empirically-driven and -- generated have erroneously interpreted and/or reported statistical results and findings. The use of "authoritative statistics" and "missing numbers" is especially salient in Best's discussions in the book. Statistics and statistical values are used as 'tools' by individuals, groups or institutions to provide a valid claim to their arguments and claims. Best especially calls the reader's attention at how these numbers and statistical values attempt to "confuse" the general public, generally assuming that the popular audience would just accept a number or statistic mainly because it seems to come from a credible source, and secondarily, because readers generally do…… [read more]

Araybhata's Contributions to Mathematics &amp Algebra Aryabhata Research Proposal

Research Proposal  |  2 pages (518 words)
Style: MLA  |  Bibliography Sources: 4



Aryabhata was born in 476 AD and was known as Aryabhata I or Aryabhata the elder. Aryabhata was a member of the Kusuma Pura School and a native of Kerala which is located in the most extreme South of India. Aryabhata is one of the greatest mathematicians of all times and is considered to be the father of the renaissance of mathematics in ancient India. (Hooda and Kapur, 2001, paraphrased) Indian mathematics historically claimed great achievements before Aryabhata's time and it was Aryabhata who first had the courage to break with tradition and to find knowledge gaps and to fill these gaps with his own research and knowledge. (Hooda and Kapur, 2001, paraphrased)

Important Contributions and Achievements in Mathematics and Algebra

Dutta (2005) in the work entitled: "Mathematics in Ancient India" states that in its earlier stages, mathematics "developed mainly along two broad overlapping traditions." (Dutta, 2005) According to Dutta (2005) these two traditions are those of:

(1) the arithmetical and algebraic; and (2) the geometric. (Dutta, 2005)

Included in Aryabhata's work on Mathematics are the following:

Arithmetic - Method of inversion, various arithmetical operators (cub, cube root)

Algebra - Formulas for find the sum of several types of series; rules for finding the number of terms of an arithmetical progression; Rule of three - improvement on Bakshali Manuscript;

rules for solving examples on interest - which led to the quadratic equation. (Indian Mathematics, 2009)

II. Most Notable Contribution in Algebra

It is stated in the work entitled: "Indian Mathematics" that of all…… [read more]

Inferential Statistics? What Are the Differences? Essay

Essay  |  4 pages (1,399 words)
Bibliography Sources: 2


¶ … inferential statistics? What are the differences? When should descriptive and inferential statistics be used?

Descriptive and inferential statistics: Summary explains the similarities and differences between descriptive and inferential stations and when each method should be used. Descriptive statistics comprises the kind of analyses to describe a study population that is small enough to include every case. Descriptive statistics can also describe the actual sample under study, but allow a researcher to extend conclusions to a broader population.

With descriptive statistics, a researcher can describe how issues affect study groups and how variables are related in to other study groups. However, the research cannot describe how those issues affect the members of the study groups and how these variables are related in those groups. Furthermore, the researcher would not be able to conclude how the results could be generalized to all groups and would not know where the groups in the study were representative of all groups.

These shortcomings of descriptive statistics are where inferential statistics come into play.

Inferential statistics extends conclusions to a broader population by making sure the study if representative of the group the researcher wishes to generalize to. This is accomplished by choosing a sample that is representative of the group to which the researcher plans to generalize. Tests of significance confirm generalization. A Chi-Sqaure or a T-Test tells the researcher the probability that the results found in the study group are representative of the population that group was chosen to represent. Chi-Sqaure or a t-test gives informs the researcher of the probability that the results found could have occurred by chance when there is really no relationship at all between the variables you studied in the population.

What are the similarities between single-case and small-N research designs? What are the differences? When should single-case and small-N research designs be used?

Cooper, Heron, and Heward (2007) explain single-case and small-n research designs. These are most often used in applied fields of psychology, education, and human behavior in which the subject serves as his/her own control, rather than utilizing another individual/group. Researchers utilize single-case and small-n designs because they are sensitive to individual organism differences vs. group designs which are sensitive to averages of groups. Small-n research includes more than one subject in a research study, but the subject still serves as his/her own control just like in the single-case design.

Single-case and small-n research have three major requirements (Kazdin):

Continuous Assessment: The research repeatedly observes the behavior of the individual over the course of the intervention. Thus, any treatment effects are observed long enough to convince the researcher that the treatment produces a lasting effect.

Baseline Assessment: Before the treatment is implemented, a researcher looks for behavioral trends. If a treatment reverses a baseline trend (e.g., things were getting worse as time went on in baseline, but the treatment reversed this trend) this is considered powerful evidence suggesting (though not proving) a treatment effect.

Variability in Data: Because behavior is assessed repeatedly, the single-subject/small-n… [read more]

Mathematics Education Term Paper

Term Paper  |  2 pages (677 words)
Style: APA  |  Bibliography Sources: 2


Mathematics Education

The objective of this work is to describe five specific methods of questions and strategies that encourage students to discuss their ideas, procedures, rules and definitions that they used to solve a problem and to discuss at least four ways in which justification of solutions to improve students' relational understanding of mathematics.

The work of Jones (2000) entitled: "Instructional Approaches to Teaching Problem Solving in Mathematics: Integrating Theories of Learning and Technology" states that: "Problem solving is defined by Kantowski as 'a situation for which the individual confronting it has no readily accessible algorithm that will guarantee a solution." (2000) NCTM standards define problem solving as "the process by which students experience the power and usefulness of mathematics in the world around them." (Jones, 2000)the stages of problem-solving are stated to be:

Understanding the problem;

Making a plan;

Carrying out the plan;

4) Looking back. (Jones, 2000)

There are five strands of mathematical proficiency, which are stated to be those as follows:

conceptual understanding;

procedural fluency;

strategic competence;

adaptive reasoning; and Productive disposition. (Taplin, nd)

Conceptual understanding of mathematics involves comprehension of mathematical concepts, operations and relations. Procedural fluency involves skills in carrying out procedures in a flexible, accurate, efficient and appropriate manner. Strategic competence involves the ability to formulate, represent, and solve mathematical problems. Adaptive reasoning involves a capacity for logical though, reflections, explanation and justification. Finally productive disposition involves the habitual inclination to see mathematics as sensible, useful and worthwhile, coupled with a belief in diligence in ones' own efficacy.

Five specific strategies that teachers may use for encouraging students to discuss their ideas, procedures, rules and definitions that they used to solve a problem include those as follows:

1) the teacher provides just enough information to establish the intent of the problem;

2) the teacher accepts right or wrong answers in a non-evaluative manner;

3) the teacher guides, coaches and asks insightful questions;

4) the teacher intervenes when appropriate and when not appropriate the teacher allows the students to make their own way;…… [read more]

Statistics Being Studied Essay

Essay  |  3 pages (869 words)
Bibliography Sources: 3


For example, it cannot be interpreted the age of the different immigrant groups, as this is not published. In addition, no conclusions can be definitively drawn about the timing of immigration flows -- those are only guessed at. In addition, there are no statistics provided in this report about the economic condition of immigrants or their settlement patterns. No conclusion can be drawn about the age of native speakers, with respect to determining the risk those languages face of extinction. The age of native speakers can be reasonably guessed, but not on the basis of the data provided in this report.

4. These statistics could impact our perception of certain topics by delivering facts about the subject. By providing accurate information, the basis is formed for the reader of the statistics to understand the facts surrounding an issue. Many topics become either politicized or subject to erroneous assumptions. Both can be countered with the use of facts. There is often a gap between perception and reality, but by understanding the reality a new and more accurate perception can be created. This will benefit anybody studying these issues, as they are able to separate out the facts from the perceptions more easily.

5. There are a number of predictions for the future that can be made using these statistics. Such conclusions can be drawn in particular if the figures from the previous census are also made available. With the 2001 figures, trends can be determined in the populations of different ethnic groups. This can assist with a number of public functions in particular, such as English or French as a second language provision and other public service provisions. If trends on ethnic diversity and language use are known, then stakeholders can better understand the ethic makeup of Canada going forward, allowing for better decisions both in terms of public policy and commerce.

The figures also include statistics on age, which is critical for both government and commerce. The degree to which the Canadian population is aging is worth understanding because of the public policy implications as well. On a general level, any line of information contained within the demographic report can be extrapolated into the future to understand the demographic trends within the country.

Works Cited:

StatsCan. (2006). Selected demographic, cultural, educational, labor force and income characteristics. Statistics Canada. Retrieved May 23, 2011 from http://www12.statcan.gc.ca/census-recensement/2006/dp-pd/tbt/Rp-eng.cfm?LANG=E&APATH=3&DETAIL=0&DIM=0&FL=A&FREE=0&GC=0&GID=0&GK=0&GRP=1&PID=99016&PRID=0&PTYPE=88971,97154&S=0&SHOWALL=0&SUB=0&Temporal=2006&THEME=70&VID=0&VNAMEE=&VNAMEF=… [read more]

Statistic Project Term Paper

Term Paper  |  2 pages (496 words)
Bibliography Sources: 1


Stat Abuse

The Precautionary Principle

Peter T. Saunders of the Mathematics Department of King's College, in London, published an article titled "Use and Abuse of the Precautionary Principle" that deals with a highly specific and unique problem when it comes to the use of statistical information. Many statistical abuses occur when conclusions not fully supported by statistics are asserted, or when differences that are not statistically significant are made to appear greater than they really are. According to Saunders, there are certain situations where it is actually good to use statistics in this way -- specifically, in cases where there is a potential for harm if a correlation exists. That is, things like cigarettes and possible carcinogens should be assumed to be unsafe as soon as any evidence suggests that they might be, unless there is a compelling reason that a potentially harmful substance should be used. Saunders advocates and over-reaction to statistical data in such cases as a means of offering the greatest protection. This is called the "precautionary principle," and it is common sense according to Saunders' explanation. In situations where the precautionary principle applies, any observed change on a population should be taken as a sign that the substance/action/etc. is correlated with that change until it can be positively demonstrated that this is not the case.

After explaining the precautionary principle in great deal and making the foundational logic and ethicality behind this principle quite clear, Saunders turns to how statistics can be abused when…… [read more]

How Statistics Apply to Entrepreneurship Essay

Essay  |  2 pages (620 words)
Bibliography Sources: 0


¶ … hear the word "statistics," the daily infographic on the cover of the U.S.A. Today comes to mind for many people. This is because they have an untrained concept of a tool with usefulness and predictive power that is difficult to overstate. In school, in public life at large and as an entrepreneur, descriptive and inferential statistics, and the ability to express and interpret the results, will become more rather than less important in innumerable ways. Essentially, statistics allows us to make accurate predictions, and thus identify and prevent wasted time and materials, and prevent potential harm to very real individuals every day.

Descriptive statistics literacy is invaluable for every day life, when the media is filled with claims about population or environmental change, or advertising trying to convince us products are safe, provide certain nutrition or what have you. For example, many people go through life thinking the more times an experiment is performed, the greater chance there becomes of a particular outcome -- I actually have a friend who thinks if he buys more lottery tickets with the same number on them, that will increase the likelihood of the number coming up! Mandating learning one simple but fundamental law of probability, that a tossed coin can keep coming up heads regardless what the prior outcomes were, could prevent very real waste. Understanding this as an entrepreneur will prevent needless experimentation trying to find production processes or material flaws where such replacement confounded identification.

Likewise for the display power of descriptive statistics, if production processes and experimental results can be expressed in complex but intuitive and easily understood scatter, box-and-whisker and best-fit plots, or histograms and bell curves of varying normality. Of course understanding this information depends on the basic concepts of dispersion and central tendency, and the general literature is full of claims based on mistaken use…… [read more]

Statistics: A Question Unanswered Term Paper

Term Paper  |  5 pages (1,450 words)
Bibliography Sources: 0


Statistics: A Question Unanswered

Before there can exist any intelligent discussion with respect to the topic of statistics one must understand that a statistical process does not stand alone nor does it function without being a part of a much larger plan, namely, research investigation as a whole. Statistics and their accompanying processes are only one such part of the… [read more]

Statistics Anxiety and Graduate Students Term Paper

Term Paper  |  4 pages (1,160 words)
Bibliography Sources: 0


STATISTICS ANXIETY and graduate students in the social sciences

Many graduate students in the social sciences need to take statistics as part of the academic training, but these students often do not necessarily have backgrounds in statistics or mathematics from their undergraduate degree or other graduate training. In the classrooms, statistics anxiety is noticeably prevalent among graduate students whose academic background has little statistical training. According to Onwuegbuzie. Slate, Paterson, Watson, and Schwartz (2000), 75% to 80% of graduate students appear to experience uncomfortable levels of statistics anxiety. As a result, conducting statistics is often rated as the lowest skill in terms of academic competence (Huntley, Schneider, and Aronson, 2000).

Statistics anxiety has been defined simply as anxiety that occurs as a result of encountering statistics in any form and at any level (Onwuegbuzie, DaRos, & Ryan, 1997), and has been found to negatively affect learning (Onwuegbuzie & Seaman, 1995). Many researchers (Lazar, 1990; Lalonde & Gardner, 1993; Onwuegbuzie, 2000b) suggested that learning statistics is as difficult as learning a foreign language. On the other hand, statistics anxiety sometimes is not necessarily due to the lack of training or insufficient skills, but due to the misperception about statistics and negative experiences in a statistical class. For instance, students often think they do not have enough mathematics training so that they cannot do well in statistical classes. With fear of failing the course, they delay enrolling in statistics courses as long as possible, which often leads to failure to complete their degree programs (Onwuegbuzie, 1997). The lack of self-efficacy and higher anxiety in statistics keep many students away from engaging in research work or further to pursue an academic career. Therefore, statistics becomes one of the most anxiety-inducing courses in their programs of study (Blalock, 1987; Caine, Centa, Doroff, Horowitz, & Wisenbaker, 1978; Schacht & Stewart, 1990; Zeidner, 1991).

A growing body of research has documented a consistent negative relationship between statistics anxiety and course performance (Zeidner, 1991; Elmore et al.,1993; Lalonde & Gardner 1993; Onwuegbuzie & Seaman 1995; Zanakis & Valenza1997). In fact, statistics anxiety has been found to be the best predictor of achievement in research methodology (Onwuegbuzie et al., 2000) and statistics courses (Fitzgerald et al., 1996). Most recently, Onwuegbuzie (in press b), using pathanalytic techniques, found that statistics anxiety and expectation play a central rolein his Anxiety-Expectation Mediation (AEM) model, being related bi-directionallyto statistics achievement and, at the same time, moderating the relationship betweenstatistics achievement and research anxiety, study habits, course load, and thenumber of statistics courses taken. The AEM model is presented in Figure 1.Onwuegbuzie (in press b) posited that the pivotal role of statistics anxiety in theAEM model suggests that Wine's (1980) Cognitive-Attentional-Interference theorycan be applied to the field of statistics, as it can be to the foreign language learningcontext. According to Onwuegbuzie, Wine's theory predicts that anxiety interferes with performance by impeding students' ability to receive, to concentrate on, and toencode statistical terminology, language, formulae and concepts. Moreover, Onwuegbuzie theorised that anxiety reduces the… [read more]

Aesthetic Appeal of Mathematics Term Paper

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From conch shells to chrysanthemums: nature abounds with spectacular arrays of geometrical forms. Their visual forms can be translated into mathematical equations, enabling an intellectual understanding of the ways such geometric forms are created and replicated throughout the visual world. Translating visual forms into equations does more than satisfy thirst for computation, though. As the "science of total intellectual order," mathematics enables human beings to perceive order in the universe, to see neither a random collection of petals nor a smelly set of sea creatures ("Patterns, Order, and Chaos," p. 189). In addition to helping human beings perceive natural order in a frequently chaotic universe, mathematics also encourages several key functions including generalization, idealization, and abstraction. The equations the mathematician conceives can be applied to all similar conch shells, not just one or two; in fact, any spiral will follow certain trajectories and will be represented through similar mathematical symbols. Equations also stimulate the innate fascination with the ideal and the absolute. Circles, pyramids, spirals, and parabolas are transformed into ideal, nearly spiritual absolutes: like Plato's forms they are archetypal representations. Represented in the mundane world, circles, pyramids, spirals and parabolas are rarely as perfect as they are in the human mind. Finally, mathematics encourages abstraction, which liberates the mind to pursue open-minded and free thinking. Mathematics reveals the beauty of the natural world and by using mathematical equations human beings can create works of majesty and art.

S. Jan Abas notes that geometric forms predominate in medieval Islamic art not only because of the admonishment of anthropomorphized depictions of deity but also because of the intrinsic aesthetic value of mathematics. The stars and rosettes that pepper Islamic art and architecture serve several key symbolic and practical functions: they symbolize divine presence and intervention; they represent divine light and spiritual illumination; and they permit actual light to flow through physical spaces such as in mosques or palaces. The aesthetic value of the star patterns in Islamic art and…… [read more]

Growth of Mathematics Term Paper

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Growth of Mathematics

Mathematics Hard and Soft

Mathematical truth is time-dependent, although it does not depend on the consciousness of any particular live mathematician," (p. 415). In other words, mathematics grows as the body of human knowledge grows; each generation gleans new wisdom from the environment, experimentation, or personal experience and transmits that knowledge to contemporary and future generations either orally or in writing. Noted mathematicians may get their names printed in textbooks or permanently etched on the name of their theorems but the greater body of mathematics grows whether or not momentous discoveries warrant an individual mathematician's fame. One of the primary ways mathematics changes over time is through the transformation of soft sources of information such as common knowledge, intuition, or hunch, into hard information in the form of proof.

In fact, mathematicians have accepted hunches and other soft sources of information to be "true" even before formal proof has been established. Number theory is especially full of instances in which mathematicians can rely fairly well on assumptions without demanding full proof: "in number theory, there may be heuristic evidence so strong that it carries conviction even without rigorous proof," (p. 411). For example, mathematicians do not know for sure whether or not an infinite number of twin prime number pairs exist and yet we still act as if there are an infinite number of twin prime pairs. Mathematicians take some ideas for granted, unless of course the ideas are proven wrong. In any case, proofs often take generations or even centuries to manifest. Prime number theory was first postulated in 1792 by a fifteen-year-old Gauss, but the theory remained unproven until 1896. Mathematicians rely on soft information that can be best described as working knowledge until hard information becomes available.

Similarly, mathematicians permit the existence of underlying beliefs, biases, and ideology that may influence…… [read more]

Mathematics as a Creative Art Term Paper

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Mathematics as Creative Art

P.K. Halmos waxes poetic about mathematics, claiming that not only does mathematics present practical value but also that "mathematics is an art" (p. 379). Envisioning mathematics as art affirms the creative potential of math and acknowledges the myriad ways math becomes manifest in everyday life. What Halmos refers to as "mathophysics" includes the applied principles of "mathology." Moreover, Halmos claims that "mathematics is very much alive today," a statement as true in 1968 when Halmos wrote "Mathematics as a Creative Art" as it is in 2006 (p. 380).

As a math teacher married to a painter, I especially relate to Halmos' comparison of the role of the mathematician to the role of the visual artist. The mathematician's role, like that of the painter, is varied and flexible. Both the mathematician and the painter interpret the world but just as the painter is not "a camera," neither is the mathematician "an engineer,' (p. 388). At the same time, mathematics and painting both serve concrete functions, and just…… [read more]

Inferential Statistics to Evaluate Sample Research Paper

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Note that the two hypotheses we propose to test must be mutually exclusive; i.e., when one is true the other must be false. And we see that they must be exhaustive; they must include all possible occurrences. Lastly, the researcher must translate the research hypothesis into operational terms. The researcher goes on to operationally define fast tempo as being music at a tempo of 120 bpm (beats per minute) and slow tempo music as being music at a tempo of 60 bpm. In addition, a researcher has to specify how participants are going to rate the music for happiness (Hays, 1973).

8. Discuss probability in statistical reference, as well as the meaning of significance.

Probability is the likelihood of the occurrence of some event or outcome. A significant result is one that has a very low probability of occurring if the population means are equal. The probability required for significance is called the alpha level and is often .05. All results obtained by statistical methods suffer from the disadvantage that they might have been caused by pure statistical accident. The level of statistical significance is determined by the probability that this has not, in fact, happened. P is an estimate of the probability that the result has occurred by accident. Therefore a large value of P. represents a small level of significance (Moses, 1986).

In experiments one needs to define a level of significance at which a correlation will be deemed to have been proven, though the choice is often actually made after the event. It is important to realize that, however small the value of P, there is always a finite chance that the result is a pure accident. A typical level at which the threshold of P. is set would be 0.01, which means there is a one percent chance that the result was accidental. The significance of such a result would then be indicate by the statement P<… [read more]

Lie With Statistics Huff, Darrell Book Report

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Perhaps the easiest way to distort survey results is simply to keep taking surveys of populations until the desired result is reached. The reason this result is produced is chance, however, rather than scientifically legitimate findings. The 'well-chosen' average is another example of this, whereby the survey sample is carefully selected to yield a figure desirable to 'prove' the contention of the reporter. Including or not including persons who would distort the average is another statistical lie. The presenter can also select the specific statistic that bests proves his thesis -- the mean, median or mode (the mean is the sum divided by the number of values, the mode is the number that occurs most often in the sample, the median is the 'middle' sampling of all listed numbers). For example, finding the 'average' American salary can produce wildly different results, given the discrepancies that can result between the median and the mean because of the high salaries of the small numbers of persons at the top, and other people who make very low salaries.

Words are powerful: calling something 'flimsy and cheap' sounds much worse than calling something 'light and economical,' and even the words 'practicing celibacy' can sound ominous, because of the association of the word 'practicing' with something nefarious (Huff 102-103). The language with which statistics are presented can also cause an unwitting reader to believe in them: for example, saying 'it is obvious that the pollution is killing all of the birds, because 100% of persons surveyed said they have not seen a single bird flying this year." (The persons may not have been paying attention, for example, to the birds). More seriously, Huff gives the example of a manager who wants to construct an anti-union survey. The manager collects any and all of the complaints that have arisen about the union, and uses these complaints to 'prove' that no one wants the union on the premises. However, it is very difficult to find an entity with no complaints about it at all, so the conclusion that is arrived at is fundamentally self-serving and misguided because the survey population did not say that it disliked the union (Huff 82).

Huff even derives a word to describe deliberately manipulating the hearts and minds of people with statistics: 'statisticulation' (Huff 102). Ultimately, the book's purpose is to encourage readers to 'talk back' to statistics so they can make rational, rather than irrational decisions. Stopping before buying or believing an advertisement is essential, so you can ask yourself, "is this believable' and 'what bias might the writer have?' Numbers, by virtue of being numbers, are not inherently truthful and relevant. It depends how they are used and a vague survey with little information about how it was conducted or how the 'average' was arrived at is no more accurate than a work of…… [read more]

Chinese Mathematics in Ancient China Term Paper

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As a result, there is scant trace of the advanced knowledge that characterized ancient Chinese mathematics.


Much of modern mathematics today emerges as re-discoveries of principles and techniques already applied by the ancient Chinese. Pascal's Triangle, for example, was already in use as early as the 13th century in China. The Chinese had also unknowingly employed the mathematical principles of the ancient Greeks before these works were rediscovered by European mathematicians like Carl Friedrich Gauss.

Despite their early advancement, however, there is little evidence of any ancient Chinese principles on mathematics today. In contrast, ancient Arabic and Hindu principles can be discerned in the techniques and number notation system employed today.

In addition to the destruction of ancient Chinese mathematical texts, the decline of Chinese traditional methods can also be traced to Matteo Ricci, a Jesuit missionary who lived in China during the mid-16th to late 17th century. Ricci is widely credited with introducing Western mathematics to China. Ricci became proficient in Chinese language and culture. As a sign of the Chinese people's esteem for the European scholar, Ricci was allowed to visit and live in Peking, which until then had been closed to foreigners (Spence 5-9).

In addition to studying, Ricci also shared with the Chinese scholars the mathematical knowledge he learned from renowned Roman scholar Clavius. The logical construction of Euclidean elements quickly superceded traditional Chinese notations. The practical orientation of Chinese mathematics further disguised their theoretical achievements.

However, the lack of any discernible influence today should not detract from the great achievements of ancient Chinese mathematics. After all, mathematical principles also underlied the development of more popular Chinese scientific developments, such as gunpowder, principles of paper money and seismographs, which were used to measure earthquakes as early as 1000 AD. It is in these scientific and technological developments that Chinese mathematical principles continue to live.

Works Cited

Martzloff, Jean-Claude. A History of Chinese Mathematics. New York: Springer Verlag, 1997.

Needham, Joseph. Science and…… [read more]

"Basic Statistics for the Behavioral Discussion and Results Chapter

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Chapter 2

The second chapter in the book continues with having readers introduced into the world of statistics while also presenting more intricate applications that they can address while using diverse calculations. This chapter is focused on having readers comprehend that experience is one of the most significant concepts when considering life as a whole. When taking into account the topic under discussion statistics can be best understood as a result of engaging in numerous calculations and as a consequence of trying to use these respective calculations with the purpose of solving issues that can emerge from rather simple activities.

Using statistics and numbers in general when discussing about people can be useful, as a research can effectively provide a conclusion regarding an event happening in society or in the natural world. Statistics makes it possible for people to be more specific about their theories and to eventually be able to verify whether or not these respective theories have a basis.

Variables are brought forward as interfering factors that can influence a research process' result. "A variable is anything that, when measured, can produce two or more different scores." (Heiman 2013, p. 16) By becoming familiarized with concepts like variables, numbers being used with the purpose of discussing things that apparently have nothing to do with them, and mathematical calculations that are particularly complex, readers gradually come to acknowledge that statistics is an active part of the social order.

Works cited:

Heiman, G. (2013). Basic Statistics for the…… [read more]

Correlation and Regression Data Analysis Chapter

Data Analysis Chapter  |  3 pages (884 words)
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SPSS Statistics: Correlation & Regression

Correlation & Regression

Is there a relationship between defect rate and volume? If so, is it positive or negative?

Yes, there is a relationship between defect rate and volume. The relationship is positive, such that as volume increases, so does the defect rate (.740).

Which variable is the independent and which is the dependent variable?

The independent variable (predictor) is the volume of production, and the dependent variable is the defect rate (outcome).

Write out the regression equation and sketch it on the plot.

Predicted score = Bslope X + Bconstant

Predicted score = 0.027(X) + (-97.073)

Based on a review of the plot provided, and examining two points -- 4400 and 4000, which respectively appear to hit the Y axis at 10% and 20.7%, the slope can be calculated to be

Thus, the regression equation would be:

Predicted Score = 0.027 (X) --

54% of the variability in defect rate can be explained by differences in volume.

5. What defect rate would you predict for a shift with a volume of 4000 units?

Defect Rate = 0.027 (4000) -- 97.073

= 10.927

6. What defect rate would you predict for a shift with a volume of 9000 units?

Defect Rate = 0.027 (9000) -- 97.073

= 145.927

7. Would you expect all shifts that produced 4000 items to have the same defect rate?

No. There can still be variance.

8. What would you estimate the standard deviation of the distribution of the defect rate to be for a volume of 4000 units?

The standard deviation of the intercept is 7.819

The standard deviation of the slope is .002

The Standard Error of the Estimate is 4.92.

9. If a particular shift produced 4000 items and had a defect rate of 10%, based on the regression model what would be the residual for the shift?

-.927, as the actual defect rate is .927 below the predicted defect rate based on this model.

Question 11B

1. Yes there appears to be a linear relationship between husband and wife's education.

2. The relationship between husband and wife's education appears to be positive, such that as one increases, so does the other.

3. The slope is .620 -- such that for every unit of increase in husband's education, the wife's education increases by .62.

4. The correlation coefficient (beta) is .561.

5. There are a few outliers on the scatterplot. In most of these cases they represent husbands who have higher educations than their wives.

Question 11C

1. Husband's education = .620(X)+5.341

31.4% of the variability in husband's education can be explained by wife's education.

2. Husband's education = .620(13)+5.341…… [read more]

Mathematics for Elementary Educators Essay

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¶ … globalization and the structures of testing in the "No Child Left Behind Initiative," it is becoming even more important that K-8 teachers be prepared to teach basic concepts of mathematics that adhere to their individual State standards, but also to a rigorous, diverse, and multicultural community. In the same way that a basic level of literacy is required before pursuing upper levels of schooling, certain mathematical constructs are vital in today's complex world of computerization, science, and the synergistic approach to many core courses. For too many people, mathematics stopped making sense somewhere along the way. Either slowly or dramatically, they gave up on the field as hopelessly baffling and difficult, and they grew up to be adults who -- confident that others share their experience -- nonchalantly announce, "Math was just not for me "or "I was never good at it" (Askey, 1999, 4).

There are four basic concepts covered in the course that particularly address the issue of relevancy in mathematical pedagogy: Mathematical Standards and Practices, Algebraic Thinking and Problem Solving, Numeration Systems and Number Theory, and Rational Numbers and Applications.

Mathematical Standards and Processes -- The National Council of Teachers of Mathematics, an international organization of teachers who are focused on improving the math curriculum globally, presented new standards in 2000 designed to improve curricula, teaching and assessment. Within their rubric, six principles were established to address themes that were valid regardless of the school culture:

Equity -- There must be high expectations and support for excellence in math education from all levels; teachers, administrators, school boards, and parents.

Curriculum -- More than a collection of problems or activities, a math curriculum should be focused, well-articulated, and flow from grade to grade.

Teaching -- Appropriate and effective math teaching requires not only an understanding of math principles but of what students need to understand, and how that should be effectively communicated to them.

Learning -- Students must learn math in a synergistic, step process- each previous module must present them with tools needed to move forward and actively build a knowledge base.

Assessment -- Assessment should support the learning aspect of math and be appropriate as a tool for understanding student needs; not simply as something easy to grade.

Technology -- Adapting technology is absolutely essential in learning mathematics (NCTM, 2009).

In addition to these overall principles, five more detailed standards and expectations were identified:

Problem Solving -- Building new knowledge through problem solving in math and other disciplines that involve mathematic calculations. Be able to apply and adapt problem solving skills.

Reasoning and Proof -- Establish initial understanding a rubric of reasoning out a problem, make and investigate mathematical conjectures, develop and evaluate mathematical arguments, and use appropriate levels of reasoning for different problems.

Communication -- Be able to communicate clearly verbally and in writing mathematical principles, equations, and solutions. Analyze the mathematical thinking of peers and others and use the language of math to express computational ideas.

Connections -- Understand the relevancy and… [read more]

Carl Friedrich Gauss Research Proposal

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Carl Friedrich Gauss

This is a template and guideline. Please do not use as a final turn-in paper.


Gauss, a German mathematician and scientist, was born in 1777. His contributions range over many fields including: geophysics, electrostatics, optics, astronomy, statistics, theory of numbers, differential geometry and more. His nickname was "Prince of Mathematicians" due to his outstanding impact on so many fields of math and science, and he is noted as one of the most influential mathematicians in history. At the age of 21, he wrote Disquisitiones Arithmeticae, a work that became fundamental in making the theory of numbers a discipline. It is still used today. While still in college, at the age of 19, he rediscovered a number of quite significant mathematical theorems, and invented modular arithmetic. In 1801, astronomers had discovered a small planet, Ceres, but lost it in the heavens. Using mathematics, Gauss correctly predicted where it could be relocated, and it was rediscovered. It began his path towards becoming Director of the astronomical observatory in Gottingen, a position he held and cherished the rest of his life (O'Connor & Robertson, 1996, para. 7). He invented the heliotrope, and discovered the potential of non-Euclidean geometry, which eventually led to the research that allowed Einstein to create his theory of general relativity. In 1831, he worked with physics professor Wilhelm Weber to study magnetism and constructed the first electromagnetic telegraph (Bell, 1986, p. 255). Gauss also developed a method of delineating the intensity of the earth's magnetic field. Gauss died in 1855

Main Contribution

It being impossible to present one main contribution as Gauss's foremost effort, we can separate four areas of contribution/focus for Gauss: (Encyclopedia of World Biography, 2005)

In his Disquisitiones arithmeticae he addressed the area of quadratic residues and his own discovery of…… [read more]

Mathematic v. Conceptual Modeling Limitations of Models Thesis

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Mathematic v. conceptual modeling

Limitations of Models

Mathematical models are often the most straightforward and simple forecasters of future outcomes, but they have severe limitations as well. Not only do most mathematical models contain a certain degree of uncertainty or risk, but there is also the risk of the model itself failing (Kay 2006). Mathematical models are unable to cope with non-quantifiable input, and thus are limited both in their use and by the increased risk that a key factor has been overlooked within the model itself (Kay 2006). Conceptual models are inherently adaptable, more able to account for the complexities of the real world and less fixed in their operations (Aspinall 2007). Conceptual models can often be used as a starting point for interactive with the model's user and the available information, allowing the model to be adjusted and still effective when situations change, as opposed to mathematical models which often have to be scrapped in their entirety when information or situations change (Aspinall 2007).

It has been said that…… [read more]

What's Math Got to Do With it by Jo Boaler Research Paper

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¶ … Math Got to Do With it? By Jo Boaler

Boaler, Jo. What's Math Got to Do With It? Helping Children Learn to Love Their Least

Favorite Subject -- and Why It's Important for America. New York: Viking, 2008.

Very often, students will whine in math class: 'when will we ever use this in real life?' This explains the… [read more]

Professional Mathematical Societies Thesis

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Professional Mathematical Societies

The American Mathematical Society which was founded in 1888 in order to further mathematical research and scholarship today fulfills its mission through programs and services that promote mathematical research and those uses strengthen mathematical education. It fosters awareness and appreciation of mathematics and its connections to other disciplines and to everyday life. The Society currently has over 32,000 individual members and 550 institutional members in the United States and around the world. It has programs and services for members and the mathematical community that include professional programs such as meetings and conferences, surveys, and employment services. It has publications including Mathematical Reviews, journals, and over 3,000 books in print (About the AMS, 2009).

The Mathematical Association of America is the largest professional society that focuses on the availability of mathematics at the undergraduate level. When it first was started it was a publication known as American Mathematical Monthly, which was founded in 1894 by Benjamin Finkel. When it became more than just a monthly publication it's structure was more of a club. The main purpose was the publication of the Monthly paper. There was one standing committee, which was the Committee on Sections, which is still the only committee that is mandated by the bylaws today. The MAA has grown tremendously over the last hundred years into a complex organization with 27,000 members. It is governed by a 50 person Board of Governors with a nationally elected President and two Vice Presidents. It currently has three peer reviewed journals, and student magazine and a newsletter, an online digital library, and, a highly regarded book publication program (Straley, 2009).

The National Council of Teachers of Mathematics is an organization that strives to be the public voice for mathematical education. It offers vision, leadership and professional development in order to support teachers in making sure that there is equitable mathematics learning for all students. The National Council of Teachers of Mathematics Board has adopted the following priorities on which the organization is run. 1. It provides guidance and resources for establishing and performing mathematics curriculum that is coherent, focused, well articulated and consistent with Principles and Standards for School Mathematics. 2. It develops and actively promotes a culture of equity in every aspect of mathematics education. 3. It engages in political and public advocacy to focus decision makers on improving learning and teaching mathematics. 4. It seeks to advance professional development by creating a coherent framework of audience-specific products and services. 5. It strives to bring existing research into the classroom, and identify and encourage research that addresses the needs of classroom practice (Mission and Goals, 2007).

The Society for Industrial Applied Mathematics is an international organization of professionals, which was incorporated in 1952. It has an interest in mathematics…… [read more]

Statistics Allowable With Nominal, Ordinal and Interval Thesis

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¶ … statistics allowable with nominal, ordinal and interval scales.

Nominal is a counting operation and its descriptive statistics is "frequency in each category, percentage in each category mode." Ordinal is a rank ordering and its descriptive statistics is "median range, percentile ranking." Interval is an arithmetic operation on intervals between numbers and its descriptive statistics is "mean, standard deviation and variance." Understanding descriptive statistics necessitates specifically looking at the type of data that are being described. The nominal scales only place numeric labels on non-quantitative concepts, for example, dogs have the value of "1" and cats have the value "2." Many categories or groups are actually nominal, such as racial group and gender. In some research, for instance, the study counts the number of individuals who are in a specific category, such as living in a designated city. Ordinal scales are ranked in a way that compares one to another, with a highest and lowest. An example is the tallest and shortest children in the school. It is not possible to perform ordinal data with mathematical computations. Interval scales allocate specific values to something, so that the intervals are equal, such as a six-point attitudinal scale. In this case, mathematical operations can be performed. With ratio scales, there is the interval with a true zero point, such as weight or the number of something in a room. Then ratios can be determined.

Difference between validity and reliability. The purpose of conducting a study is to come up with accurate measurement results. This is why research must be both reliable and valid; the two are interrelated. Reliability is the consistency of the measurements, or how well the study can be repeated. Does the same measurement yield the same results when repeated? Reliability cannot be calculated, only estimated. Validity is whether the test is measuring what it expects to measure. if, for example, the researchers are measuring a table that is six feet wide, they measure the table with a measuring tape and find it is six feet. They measure it again and again and consistently get six feet. The tape measure is yielding reliable results. The tape measure includes inches and feet, so it should also yield valid results. If the researchers measure the table with the "right" tape measure, it should yield a correct measurement of the table's width. In other words, when conducting research, it is necessary to use measurement tools that yield consistent responses when asked time after time and that yield accurate responses from the participants.

Difference between conceptual and operational definition. Conceptual definitions define a concept with the use of other concepts, which makes measuring difficult. An operational definition specifically identifies at least one observable condition or event, so the researcher knows how to measure that condition or event. The operational definition must be reliable and valid. For instance, if a researcher wanted to know about a person's enjoyment for his or her job, the conceptual definition would reflect interest for an enjoyment and satisfaction… [read more]

Blaise Pascal Biography Thesis

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Blaise Pascal Bio

Blaise Pascal's Biography

Blaise Pascal was a French mathematician, physicist, and religious philosopher. As a person, Pascal integrated different qualities in a nearly inconsistent manner. He held a position of basic skepticism, directed not in favor of that of Descartes, who was employing primary philosophical doubt only to get hold of a secure basis for his philosophy.… [read more]

Statistics for Social Sciences Correlation Term Paper

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Statistics for Social Sciences


This assignment was designed to help students 1) develop a deeper understanding of the purposes of correlational techniques and 2) become more familiar with hand-computed and computer-based correlational analyses.

Use the smoking data provided to complete the following steps. NOTE: you can copy and paste the data into SPSS if you use the electronic word file of this assignment I have sent. Show all your computational work.

Hand compute the correlation between the number of years smoking (YR.SMOKE) and the number of cigarettes smoked per day (CIG.DAY).

Hand calculate the correlation between the number of cigarettes smoked per day and the level of carbon monoxide expired (CO.LEVEL).

Report both correlation coefficients and describe the strength and direction of each in words (based on Tables 5.1 and 5.2 in text).

d. Calculate the coefficients of determination and alienation for both correlations and explain what the numbers mean.

e. Draw two Venn-like diagrams similar to those in Figure 5.5 (p. 90) to demonstrate the coefficient of determination for both correlations.…… [read more]

Neuman ), Researchers Frequently Need to Summarize Term Paper

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¶ … Neuman (2003), researchers frequently need to summarize information concerning one variable into a single number for which they use a measure of central tendency. Measures of central tendency are those descriptive statistics that describe the point or points about which a distribution centers. This paper provides a description of the three measures which are used to describe central… [read more]

Aristotle and His Contribution to Mathematics Term Paper

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¶ … Aristotle and his contribution to mathematics and mathematical concepts. Specifically it will discuss his life and contributions, including other mathematicians he worked with or influenced. Aristotle, one of the greatest philosophers and mathematicians of all time, lived from 384 B.C. To 322 B.C. He was born in Macedonia, and spent most of his adult life in Greece as a student of Plato, and then as a teacher and philosopher. He also lived on the island of Lesbos for a time, and was the teacher of Alexander the Great for a time. He also tutored Eudemus of Rhodes, who wrote a history of geometry, and Theophrastus of Lesbos (Lane). He died at the age of sixty-three in Chalcis, after being exiled from Greece for being "anti-Greek."

Aristotle is not thought of primarily as a mathematician, but rather a philosopher and biologist or scientist. In fact, many historians believe he actually left the Academy of Plato because he placed too much of an emphasis on mathematics in his instruction. Plato did influence many of his philosophies, however, which means he at least indirectly influenced his theories on logic.

However, Aristotle did contribute greatly to mathematics, particularly in the areas of deductive logic and geometry. One of the most famous theories he offered to geometry is that of triangles in circles. He discovered that a triangle drawn in a semi-circle is a right triangle, and this is always the case. It is one of his best known geometric theories, and one that many people consider the most valuable, because it helps define the "logical" rules of geometry that define this area of mathematics. Logic was perhaps his greatest contribution to mathematics, because it made the science of mathematics more effective and easier to understand.

Aristotle wrote heavily on logic, and how to apply logic to the sciences, such as mathematics. He wrote his theories in the "Organon," which contained six different treatises about logic. One writer notes, "Organon' is the Greek word for 'tool,' and this title expresses the idea that these six…… [read more]

George Polya Term Paper

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George Polya

The Hungarian mathematician, George Polya, is hailed by many as not only one of the greatest mathematicians, but also a great teacher of his time. It is interesting that his early school career did not mark a very high interest in the field, however. Later, when faced with choice, his mother encouraged him to take a career in law like his late father. When examining his biography, the reader becomes aware of Polya's extraordinary ability to face and overcome difficulty in order to attain his dreams. This trait, as will be seen, was something his father also possessed.

Polya's parents, Anna and Jakab, were both Jewish. Jakab's original surname was in fact Pollak, but he changed this for the sake of his professional goals. After his law firm failed, hw worked for an international insurance company. However, Jakab's dream was to obtain a research post at a university and pursue his true interests, economics and statistics. It appears therefore that George inherited not only his father's tenacity, but also his interest in numbers. In 1882 Jakab Polya was finally appointed as Privatdozent at the University of Budapest.

George's parents converted to the Roman Catholic faith in 1886, a year before his birth, and he was subsequently baptized in the Roman Catholic Church. George grew up in a home with four other children, three of whom were older than himself and one younger. Jeno, who was the eldest, loved mathematics, but pursued medicine, distinguishing himself in this field as prominently as George did in mathematics. Laslo, the youngest, was considered the brightest of the children, but was killed in World War I before having the opportunity to distinguish himself.

During his schooling at the Daniel Berzsenyi Gymnasium, George studied languages, biology, mathematics, geography, and other required subjects for young children. His favorites were biology and literature, where he received "outstanding grades."

As mentioned above, Polya was not greatly interested in mathematics during his early school career. Many critics ascribe this to the quality of teaching he received in this field. Indeed, he described two of the three mathematics teachers at the Gymnasium as "despicable." His grades were also not particularly high, although he did well in arithmetic.

By the time when Polya enrolled at the University of Budapest in 1905, his brother Jeno was a surgeon, and could support his study efforts financially. Although at first pursuing study in law as his mother wished, George found this extremely boring and gave up after only one semester. After this, he changed his direction to languages and literature for two years, gaining a certificate for his trouble. After this, Polya was interested in pursuing philosophy, but was advised to take physics and mathematics prior to pursuing the complicated subject.

This finally put him on the path that would become a distinguished career.

Polya studied at the University of Vienna during 1910-11, and attended mathematics lectures by Writinger and Mertens. During this time, he also continued pursuing his interest in physics by… [read more]

Science if Conducting an Experiment Term Paper

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Bibliography Sources: 3


¶ … science if conducting an experiment that can allow the experimenter to make reasonable inferences about the material described. This paper describes different aspects of the experimental process. It discusses descriptive and inferential statistics; single case and small N. research designs; true experiments and experimental designs; and qausi-experiments. It discusses the relative strengths and weaknesses of each experimental approach.

What are the similarities between descriptive and inferential statistics? What are the differences? When should you use descriptive and inferential statistics?

Descriptive statistics refers to data that describes, shows, or summarizes data in a meaningful way (Lund Research Ltd., 2012). Descriptive statistics present the data, but they do not allow one to make conclusions about data. In other words, descriptive statistics can be described as a way to organize raw data. There are two main types of descriptive visits that are most relevant: measures of central tendency and measures of spread (Lund Research Ltd., 2012). Descriptive statistics are frequently summarized in tables, charts, and graphs, which make it easy to see the general results of a study. "Descriptive statistics are applied to populations and the properties of populations, like the mean or standard deviation, are called parameters as they represent the whole population (i.e. everybody you are interested in)" (Lund Research Ltd., 2012).

Inferential statistics is a means of translating descriptive statistics and trying to apply it to a large group, when one does not have access to an entire population. "Inferential statistics are techniques that allow us to use these samples to make generalizations about the populations from which the samples were drawn. It is, therefore, important the sample accurately represents the population. The process of achieving this is called sampling. Inferential statistics arise out of the fact that sampling naturally incurs sampling error and thus a sample is not expected to perfectly represent the population. The methods of inferential statistics are (1) the estimation of parameter(s) and (2) testing of statistical hypotheses" (Lund Research Ltd., 2012).

One would use descriptive statistics to present the information received from a specific population. Descriptive statistics are clear, but they only allow one to present information about those things that were actually measured. Inferential statistics have a margin of error, but allow the researcher to make conclusions about a broader group than was actually measured.

2. What are the similarities between single-case and small-N research designs? What are the differences? When should you use single-case and small-N research designs?

Single case research design is a design that is frequently used in applied psychology, and is when a subject serves as his own control group. The goal of the single-case research design is to examine the impact of a variable on the subject. "Single-case research is idiographic rather than nomothetic" (Brogan, Unk.). There are several features of a single-subject design including: baseline assessment to determine the status quo before an intervention is applied, and continuous assessment to determine the impact of the intervention.

Many people use the term small-N research design interchangeably with… [read more]

Descriptive Statistics Data Analysis Chapter

Data Analysis Chapter  |  2 pages (687 words)
Bibliography Sources: 2


¶ … Attitude Nature

Nature Stats Attitudes

Table 1 (Appendix I) displays the results of a survey of students asked to rank their attitude toward nature on a continuous integer scale of 1-100. The results present a clear picture of these students' attitudes and also inform further question about their outdoor activities in a number of ways. The results in Table 1 support future hypothesis testing because skewness and Kurtosis are close to normal, which indicates both parametric and non-parametric inferential statistics will likely be appropriate to describe and predict correlation between other variables of interest, which is often not the case for samples this small (n=30).

Table 2, "Attitude About Nature" (Appendix II) lists the frequency of students' ranking of their attitudes for nature, against which other variables can be compared to see if the resulting distributions are statistically significant, i.e. occur as much or less often than would occur by chance at whatever degree of "alpha" or risk of Type I vs. Type II error experimenters decide is of interest, usually 0.05 or 0.01. The results demonstrate that no student answered below the value of 5, and since the top score was 100, therefore no student could answer more than that, which bodes well for the normality of data since this reduces the effect of outliers, which shows up in low skewness and Kurtosis near to normal (below). While the distance between the one "100" answer and the next-highest group of two "80" answers suggests the "100" could possibly be an outlier introducing enough skew to demand non-parametric inferential tests, a number of tests easily performed in SPSS will demonstrate the strength to which that sole "100" result disturbs the normality in the rest of the data.

Figure 1 (Appendix III) shows these results displayed in a frequency histogram with normal curve superimposed. This histogram reveals that the results were similar to normal, with the highest frequency occurring around the median, such that mean and median were very close, which Table 1 reveals was only a difference of one percent (Appendix…… [read more]

Bio-Statistics Research Activities, Whether Clinical Term Paper

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In other words, the authors did not build a medical or healthcare-based paradigm for the study. Following a well-defined research question the research investigators' task is to follow-up with a statement of a testable null hypothesis or hypotheses. The null form of the hypothesis is required in order for the proper application of a statistical data analysis tool to be… [read more]

Individual and the Culture Term Paper

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How Mathematics Grows: The Role of the Individual and the Culture

Influences the Course of Mathematical Discovery

There are many influences on the course of mathematical discovery. The dominant forces influencing mathematical discovery are individual and culture, as pointed out by the reading. There is as much subjectivity in mathematical computation as there is science, which is part of the reason so much of mathematics is ill understood and often misinterpreted. As the reading points out those not well versed in mathematics or those with little training often have an imperfect notion of how it operates and how solutions or mathematical proofs must be derived. Often what seems correct is later found incorrect, and vice versa. This is evidenced by the example in the reading, whereby professor Hans Rademacher of the University of Pennsylvania, a leading theoretician at the time, mistakenly believed he solved Riemann's Hypothesis (p. 60) only to be disproved later. The individual and culture directly influence mathematical discovery. There isn't really a dichotomy between the individual and culture; they simply influence mathematics differently. For example, an individual who is brilliant and capable of great mathematical feats may at the same time think outside of the scope of what the culture he or she lives within may consider "ordinary." Thus this person's brilliance or folly will either be embraced or rejected depending on the fit with the culture at the time the solution or hypothesis is presented. The reading for example, points out the case of Hermann Grassman, whose work is today considered genius, however during his time was consider obscure and mystical because the work was not in line with the culture Grassman grew up in.

The creating and practice of mathematics are not the same. The practice of mathematics is more aligned with cultural norms and what is considered acceptable practice during the time mathematics is accomplished. Creation however, may involve the extremes of an individual, or an individual's ability…… [read more]

Reaction to Proof Things Term Paper

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Mathematical Proofs middle school mathematics teacher seems at first to gain little from absorbing an article like Kleiner & Movshovitz-Hadar's "Proof: A Many Splendid Thing." However, the authors' explication on the origin of mathematical truth-finding and the changing role of the proof in mathematics reveals several key points that can incorporated into general math classrooms. For example, Kleiner & Movo*****z-Hadar discuss the confluence of philosophy and math throughout history, pointing out especially their shared use of logic and dependence on the successive logical proof in explaining their mutual discoveries to colleagues. Similarly, junior high students may be able to appreciate, if not the details of the Enormous Theorem, at least the process of thinking that underlies mathematical proof. The gap between the seemingly abstract world of theoretical math and everyday reality may not be as great as we all think. Students of math can especially benefit from a deeper understanding of the proof for the satisfaction it can bring. Mathematics is not only about measurements, calculations, and counting. Rather, mathematics form the building blocks of rational thought: our work is about process and proof.

With a firm foundation in logic, mathematics cannot be…… [read more]

Psychology What Are the Similarities Research Paper

Research Paper  |  3 pages (947 words)
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What are true experiments?

True experiments consist of more than a single purposively designed group, random assignment, and outcomes that are commonly measured. Ethnicity and sex cannot satisfy such requirements because it is impossible to manipulate them without purpose. These designs only occur when a sample is chosen in random and assigned to comparison groups and program. If the researchers can perform the experiments using random assignments, it means that the experiment programs are true designs.

How are threats to internal validity controlled by true experiments?

Bias is a menace to interior validity. It is the primary source of errors into results and measurements. Bias occurs when experimental items that are in favor of an age, ethnic group, or gender are used. Bias is a serious threat to internal validity because it creates an unconventional elucidation for the domino effect of a research conducted. True experiments can be used to control threats such as bias. True experiments control much of such threats through ensuring that the experimental treatment groups are equivalent before the study begins. This helps the researcher to control factors such as regression and self-selection towards the mean effect. In addition, true experiments are used in measuring the variables that could be potential threats thus controlling them statistically. As a result, threats to internal validity would be minimized.

How are they different from experimental designs?

True experiments are different from experimental designs in the way in which the ethnicity, the population, and sex are designed. The internal validity experiences threats when the researcher attempts to influence the results, this implies that, the mind of the researcher is partial and makes changes on the variables so that he or she can attain the desired results.

What are quasi-experimental designs?

These are research designs commonly used in making evaluations of educational programs when a practical or a random assignment is impossible.

Why are they important?

Researchers use quasi-experimental designs when they are unable to control the participants' assignment to conditions or when it is impossible to manipulate the variables. Instead, researchers make comparisons between variable in existing groups or a group of participants that already exists after and before the occurrence of a quasi-independent variable.

How are they different from experimental designs?

Quasi-experimental research designs are mostly used in making evaluations of problems in education when it is impossible to make random assignment or a practical. These designs are prone to numerous interpretation errors even though they are commonly used. Experimental research designs are highly effective in addressing the issue of evaluation about the usefulness and impacts of a program. These designs emphasize on the importance of comparative data as the basis for making interpretations of research findings. They increase the confidence of researchers showing that the findings are the results of an innovation or program and not of an…… [read more]

Quantitative Analysis for Business Essay

Essay  |  2 pages (637 words)
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¶ … Business

Statistics is the study of data collection, its organization, analysis, interpretation and eventually its presentation. It is the science of collecting, summarizing, analyzing data in numerical form. It entails planning on data collection in terms of design of surveys and experiments to be used (Calkins, 2005).

There are two types of statistics which are Descriptive statistics and inferential statistics. Descriptive statistics entails the methods of organizing, displaying and data description with the use of tables, graphs and summaries. Inferential statistics is a process that is used in the description of a population on the basis of results found. It entails estimations of unknown parameters of population that are based on sample results and hypothesis testing that is used to either accept or reject the hypothesis made prior.

There are four main levels of measurement that are used in statistics. These are nominal, ordinal, interval and ratio. They all have their own different degree of usefulness in statistics. Nominal measurements do not have any meaningful rank order among values it uses numbers and labels only. It can therefore be used to do cross tabulations for example the chi-square test is performed on cross-tabulation of nominal scale.

Ordinal measurements have difference between consecutive values that are imprecise but have meaningful order to those values.

Interval measurements have distances that are meaningful between measurements that have been defined but with a zero value that is arbitrary. They can be used in the computation of statistical measures that are commonly used.

Ratio measurements are those that have both a meaningful zero value and distance between the measurements clearly defined hence provide great flexibility in the particular statistical method used in data analysis (Calkins, 2005).

Statistics enables prediction of an event hence plays a crucial role in business decision making. It can bring about the difference between the continued success of a business and its eventual failure. Statistical research therefore…… [read more]

Numerical Research That Can Be Analyzed Essay

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¶ … numerical research that can be analyzed in a statistical fashion. Quantitative research frequently -- although not exclusively -- deploys the scientific method whereby a hypothesis is tested in a controlled fashion. One group, the experimental group, is subjected to an intervention known as the independent variable while another, otherwise similar group, is designated the control group and not subjected to that variable. The dependent variable is the change or lack of change that results from the intervention, and the results prove or disprove the initial hypothesis. Quantitative research can also take the form of a survey or other instrument designed to collect raw data about a particular population.

In contrast, qualitative research is designed to explore the evolution of a particular phenomenon in narrative form. Responses from test subjects may be coded and subjected to data analysis, but ultimately the goal of this type of research is to record the particular experience of a population in a holistic fashion, not test a theory within limited parameters. This contrast means that qualitative research is often seen as subjective, versus the superior objective claims of quantitative methodologies. However, there are many persistent problems with quantitative research that complicate this schematic notion. It has been observed that "poor statistics" make for "poor science" but this is true of all disciplines: indeed, in the social sciences, where variables are more difficult to isolate within populations, rigorous statistical methodology to eliminate error is even more significant (Gardenier & Resnik 2002: 70). Also, in quantitative research, using effective statistical testing is vital, regardless of the experiment, given the ethical implications of having human subjects, take the risk of participating in a study with questionable utility and value (Gardenier & Resnik 2002: 66).

In an experiment involving statistical analysis of a population, the formal 'null hypothesis' is tested (the theory that nothing will happen). The null is actually a statement that is contrary to what researchers want to prove. In general, it is assumed that false rejection of the null hypothesis is less damaging than false acceptance -- i.e., it is thought that overestimating the potential impact of a variable is less troubling than not recognizing its impact (Baroudi & Orlikowski 1989: 88). "The embedded null approach involves embedding a hypothesis of no effect within an interaction framework. The framework is then used to show that, under certain conditions, the manipulation/predictor variable in question does produce an effect or relationship, while under the conditions of primary interest, the effect or relationship does not appear" (Cortina 2002: 342).

The cautious approach to tracking change makes sense given that the selection of the test population may be imperfect and contain too many outliers. That is why a 'statistically significant' alteration must be in evidence, not simply any change at all. "The reason that we avoid concluding a lack of effect from studies that show minimal or non-significant results is that there are many alternative explanations for this finding" (Cortina 2002: 343). Particularly in the social sciences, it… [read more]

Division by Zero Mathematics Term Paper

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Also, since any number times zero will equal zero, there is no one unique solution for the answer. Example problems such as 2x0 = 0 and 1450 x 0 = 0 show that a number times zero equals zero. However, at the same time, zero times itself does not equal the number multiplied by zero. The answers cannot be duplicated when the reverse operation is performed (Knifong 1980,-page 179). Even 0 x 0 = 0 is problematic in that zero divided can be divided by itself and multiplied by itself an infinite number of times.

In higher mathematics, such as calculus, the question of division by zero becomes even more complicated. Asymptotes, for example, are lines which correspond to the zeroes of the denominator of a rational function (Kuptsov 2001). This is necessary in determining geometric functions because, since zero can never be in the denominator, the person solving the equation knows that the graph of their equation cannot include the numbers which would allow x to equal zero. For example, if the graph of a line were y = 2/x, x could never be zero because then 2/0 would be an undefined number. The physical presence of x unequal to zero is shown on the graph, but still the solution to a number divided by x is not visible.

Limits are another component of calculus which complicates the division of a number by zero, but still does not change the fact that it is impossibility. Even in calculus, the actual arithmetic value of zero divided by itself cannot be determined. Instead, the function of the limit is to determine a pattern of mathematical quotients to make a best estimate at what such an answer might be if it were to exist in the real world (Weisstein 2012). The established rule for calculus and limits is that the limit of division by zero can be either plus or minus infinity, or that it can have no limit. This is written as either ? Or -?. With limits, the mathematician can get close to approaching the answer to division by zero; however this is only ever an approximation and is never able to fully solve the problem.

There have been advances in mathematics, such as hypothetical and theoretical math topics, such as fractal Cantonian space time. It is an "operational extension to algebraic groups" which poses that there is a place within quantum physics which would allow for a division by zero (Czajko 2004,-page 261). Researchers in this field have postulated that this division will allow for better understanding and utilizing of "mutually dual line vector spaces" (Czajko 2004,-page 262). Scientific inquiry also poses potential situations where there may in fact be ways to divide by zero. However, it must be noted that all these propositions are theoretical and none have been empirically proven.

In common mathematics, zero is not actually a number. Rather it is the placeholder for the position between positive and negative. It is, in reality, the lack… [read more]

Grade 1 Math Standards Essay

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Through performance standards design, the two systems have developed a system of conceptual nesting rather than simply relying on the more conventional system of learning tiers. Too often, in previously employed standards for mathematics performance, students advanced through their demonstrations of mathematical reasoning by moving from one tier to the next presumably more advanced tier. For instance, first graders needed to demonstrate that they could count to 100 before they began addition, or the like. The point is that the performance standard categories were treated as discrete teaching and learning units. The approach taken by the North Carolina Teachers of Mathematics (NCTM) standards and the North Carolina Common Core state standards is integrative -- the standards do not assume that children will achieve an understanding to the numerical relationships in their instructional units. Rather, the performance standards are designed to deliberately draw and teach those relationships by coming at the constructs from any different perspectives and practical exercises.

The mathematics performance standards are part of a larger whole designed to encompass the learning requirements for students across their K-12 educational experience. These new clear and consistent state standards have been thoughtfully aligned with the expectations of higher education and the workplace. The current standards are contiguous with earlier versions of state standards, an important consideration for efficacious institutional effort in teaching and for the motivation of students. In other words, no lost time and no wasted effort results from the adoption of the new state standards.

Moreover, the state standards have been rigorously vetted through empirical research and are informed by the global standards for mathematics. Moreover, the North Carolina Teachers of Mathematics (NCTM) standards and the North Carolina Common Core state standards are referenced to rigorous content that focuses on application of higher order skills.


On 3 June 2010, North Carolina adopted the Common Core State Standards, joining the first group of states to do so. The adoption is based in the understanding that if students are to develop deep mathematics understanding, they must move well past a follow-the-rules position to make sense of what they are doing in math.


Common Core State Standards Initiative. [Webpage]. Retrieved October 19, 2012 from http://www.corestandards.org/

Curriculum and Focal…… [read more]

Organizational Health Educational Institutions Essay

Essay  |  8 pages (2,709 words)
Bibliography Sources: 8


The refrain is often heard that not enough students graduate with degrees in STEM majors, and that students in America are not able to compete with students in Canada, Finland, and South Korea who score higher on their mathematics tests than do students in the U.S. ("Business Coalition," 1998; Hacker, 2012).

Section IV: A Learning Solution Proposal

The expectation that… [read more]

Psychological Research Descriptive and Inferential Research Paper

Research Paper  |  4 pages (1,173 words)
Bibliography Sources: 3


A variable is then tested on the test group, while the control group remains unaffected. The results from the test group are then compared to the control group, which has not been involved in the actual testing, and the results are observed.

By using a "true experiment" design, the results are difficult to refute, but there are things that can invalidate a study. These are known as threats to internal validity, or "confounds that serve as plausible alternative explanations for a research finding." ("Threats to Internal Validity") There are a number of different threats which can serve as alternative explanations including what is referred to as a patient's history, maturation, the effects of testing on a subject, the instrumentation used, chance, attrition, and even the selection of subjects for the test and control groups. Some of these threats can be minimized because a true experiment must be set up in a way that will do so. For instance, making certain to randomize the individuals in the both the test and the control groups, isolating the subjects from each other to prevent interaction, keeping the testing short to minimize the chance of boredom influencing the subject's reactions, or only testing one simple variable. But despite these efforts, not all internal validity threats can be eliminated. There will always be the chance of contamination of the subjects, or interaction, rivalry, or competition between subjects. Subjects may lose interest in the study, become bored, or even resentful toward the researchers. There are also what is called expectancy errors, which are errors made by the experimenters in interpreting or analyzing data. And sometimes the subject may simply alter their view of things during the study, which may effect their responses.

4. Quasi-experiments

Quasi-experiments are an important alternative when true experiments are not possible. These types of experiments are similar to true experiments but lack the degree of control found in true experiments. Quasi-experiments usually lack a sense of randomness and are usually conducted in external environments, such as a work environment. There are usually at least two variables in quasi-experiments, the "quasi-independent variable," or the variable that is being tested, and the "grouping variable," which is similar to a control group but with a variable that has a predictable result. This predictable result will serve as the base to compare the results of the quasi-independent variable against.

These types of experiments are important when a true experiment is not possible, or when certain variables of the experiment cannot be controlled. It is also important when experimenting necessitates that the experiment be conducted outside a controlled laboratory environment. And since quasi-experiments are natural experiments, their conclusions may be applied to other subjects and settings, and used to make generalizations about an entire population. While the results of true experiments may be limited to the population studied, quasi-experimental results can be expanded to cover more than just those involved in the study. This is their real value, being used to draw larger conclusions about larger populations.… [read more]

Conselling Master Questionnaire Questionnaire

Questionnaire  |  15 pages (4,070 words)
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The primary objective of statistics is to make inferences concerning a population. In so doing, there is a need to explain or offer information concerning the sample, which will major in a given study. Descriptive statistics come in, and assist in describing the sample on which the study will take place. In addition, descriptive statistics first offer substantial information… [read more]

Artist in Cultural Phenomenon Term Paper

Term Paper  |  3 pages (810 words)
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As strange as it might seem, Aronofsky's film is meant to discuss the idea of abstract math. These are two concepts coming together and forming a paradox, as they practically enable viewers to understand that there is much more beyond calculations and simple mathematical formulae.

This film is not necessarily meant to discuss with regard to typical mathematical ideas. Instead, its producers wanted to address an intriguing idea regarding mathematics and science in general: the chaos theory. The motion picture's protagonist discovers a link between the chaos theory and the number Pi and this causes a great deal of individuals to express interest in his work. These respective people practically acknowledge the important role that this discovery could play for humanity as a whole and concentrate on understanding it themselves in order to be able to accomplish goals that would be unachievable otherwise.

Aronofsky probably wanted his viewers to realize that there is a strong connection between the world and mathematics. Mathematics can practically function as a language in explaining events happening throughout the universe and a person who is well-acquainted with this respective language is likely to gain a more complex understanding of things that seem unexplainable.

Pi is one of the most powerful concepts in the film and by looking at how the circle is a perfect shape, one can easily acknowledge that Pi has a special place in the world. By dividing a circle's circumference by its diameter, one can get the number Pi. This particular number is impressive because it would be impossible to write it by using a traditional mathematical form. Instead, people relate to it by using a symbol, thus making it possible for humanity as a whole to understand the limitations how much the world actually knows with regard to mathematics.

Aronofsky emphasized Pi as a number that goes on and on forever and that is thus impossible to understand by people. The very concept of infinity stands as an idea that people understand, but that they also find impossible to think about. Similar to the Univers, the number Pi is infinite and humanity is unable to ever understand it completely. Pi practically took this number and related to it as possibly being the answer to existential questions -- questions that people have always considered, but that they have also acknowledged as being impossible to answer.

Works cited:

Dir. Darren Aronofsky. Pi. Artisan…… [read more]

Mathematics George Cantor Term Paper

Term Paper  |  2 pages (673 words)
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When people began to understand that mathematics could influence everything from photography to art and science, they took a greater interest in mathematics and philosophical thought, which in turn led to even more innovation and scientific thinking. In fact, today, many scientists and mathematicians feel Cantor's work represented a real paradigm shift, or a radical change in mathematical and philosophical thought ("Cantor"). Two of his lasting models that showed his theories were "Cantor's Comb," which showed all points were disconnected from each other, and "Cantor's Dust," which calls these disconnected sets "fractal dust" (Breen). Cantor's work really revolutionized mathematics, and encouraged people to think philosophically about just what numbers really were.

Unfortunately, Cantor's mental health deteriorated as he aged, and he had several nervous breakdowns in reaction to criticism of his work. Today, many believe he suffered from bipolar disorder ("Cantor"). It is sad to think that Cantor may have contributed even more to the mathematical world had he not suffered from mental disorders, as he often stopped working during his bouts with depression.

Another German mathematician, David Hilbert, described Cantor's work as "the finest product of mathematical genius and one of the supreme achievements of purely intellectual human activity" (O'Connor and Robertson). Cantor's theories changed the way mathematicians thought about infinity and sets, and translated into many areas of society. Cantor's work is still questioned and studied today, but the importance of his theories is not questioned.


Author not Available. "Georg Cantor." Fact-Index.com. 2004. 13 April 2004. http://www.fact-index.com/g/ge/georg_cantor.html

Breen, Craig. "Georg Cantor Page." Personal Web Page. 2004. 13 April 2004. http://www.geocities.com/CollegePark/Union/3461/cantor.htm

Everdell, William R. The First Moderns: Profiles in the Origins of Twentieth-Century Thought. Chicago: University of Chicago Press, 1997.

O'Connor, J.J. And Robertson, E.F. "Georg Cantor." University of St. Andrews. 1998. 13 April 2004. http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Cantor.html

Transfinite Number." Van Nostrond Company, Inc. Van Nostrand's Scientific Encyclopedia. Princeton: Van Nostrand, 1968.… [read more]

Prediction Essay

Essay  |  6 pages (1,807 words)
Style: APA  |  Bibliography Sources: 0


38; median = 3.3; mode = N/A (all values at the same frequency); variance = .692889; standard deviation = .263228; kurtosis = -1.2189; skew = .182109; range = 2.5; sum = 38.3.

Higher reaction time memory score group: being = 9.24; median = 8.85; mode = 9.5; variance = 5.004889; standard deviation = 2.237161; kurtosis = 6.86883; skew = 2.443916; range = 7.9; sum = 94.2.

Aside from the obvious difference is one would expect when separating groups into low and high scores (e.g., higher/lower mean, median compared to the overall group results, different sum, etc.) there are a couple of interesting differences here. First, the lower reaction time group does not have a specific mode (although scores in the distribution at the same frequency of occurrence, thus there are multiple modes), whereas the higher reaction time group at a specific mode. The presence of an outlier (X = 15.2) in the higher group score inflates the mean, the range and the variance in the second group (thus any descriptive statistics using the sum of the scores would also be inflated by an outlier in the high range). For instance removing the high score reduces the mean, standard deviation, range, and sum and of course the shape of the distribution would also be affected.

The measures of central tendency are unaffected when you double the same scores in each data set. This is because you are just simply adding more of the same score and you are not adding a lot of variance to the sample. Of course the sum changes significantly because you are doubling it. There are some slight changes in the measures of dispersion due to the fact that the variance decreases when you add the same score to a distribution of scores. The shape of the distribution will also change slightly as…… [read more]

Determining Appropriate Statistics Methodology Chapter

Methodology Chapter  |  2 pages (860 words)
Bibliography Sources: 2


¶ … Kolmogorov-Smirnof test

Factor analysis

Linear regression

Goldfeld-Quandt test

Kaiser-Meiyer-Oklin (KMO)

Multivariate regression

Correlation -- Pearson's r

Cronbach's ?

Durbin-Watson statistic

See descriptions and justifications below.

Correlation importance and justifications

Correlation measures the strengths of association between two variables and, as such, enables the performance of bivariate analysis ("Statistics Solutions, 2012"). The value range of the correlation coefficient extends between +1 and -1. A correlation coefficient of ± 1 indicates a perfect degree of association between the two variables. Assumptions for the Pearson r correlation include normal distribution, linearity, and homoscedasticity ("Statistics Solutions, 2012"). Linearity assumes a straight line relationship between each of the variables in the analysis and homoscedasticity assumes that data is normally distributed about the regression line ("Statistics Solutions, 2012").

3. Reasoning (justifications) to use parametric or non-parametric statistics

Parametric statistics are used when the data is expected to show a type of probability distribution from which inferences can be drawn based on the parameters of that distribution (Geisser & Johnson, 2006). More assumptions are made when using parametric methods than non-parametric methods, which can generate more precise and accurate estimates if the assumptions are correct; this is known as statistical power (Geisser & Johnson, 2006).

4. Selection of statistical method suitable for the selected model(s) And 5. Justification of the selected statistical method

Multivariate analysis is used because there are so many independent variables. This is already discussed in the draft of the paper.

6. Assumption of the selected statistical method(s) AND 7.Discuss the need of Normality assumption

With parametric statistics, there is an assumption that the data will be based on normal probability distributions that have the same shape and are characterized (parameterized) by a mean and standard deviations ("Statistics Solutions, 2012"). That is to say, if the researcher knows the mean and standard deviation -- and if the distribution is, in fact, normal -- then the probability of any future observations can be known ("Statistics Solutions, 2012"). To verify data normality, a goodness of fit test may be used; in this study, the Kolmogorov-Smirnof test will be used ("Statistics Solutions, 2012").

7. Multicollinearity assumption & implication to student work

Multiple linear regression assumes little to no multicollinearity in the data. When independent variables are not independent from each other, multicollinearity exists ("Statistics Solutions, 2012").. There is also an assumption of independence regarding the error of the mean ("Statistics Solutions, 2012"). That is to say that the standard mean error of the dependent variable is independent from the independent variables ("Statistics Solutions, 2012").

8. Discuss ways to overcome the Multicollinearity

When multicollinearity occurs in…… [read more]

Course Analysis: Math and Statistics Term Paper

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Bibliography Sources: 3


Statistics can be described as the study of the collection, interpretation, presentation, description and analysis of data. In particular, statistics in business taught us to apply a variety of statistical methods in a business context to facilitate evidence-based decision making and to provide answers to business related questions. The overarching objective of the course was to analyze each of the course elements in detail and at the same time learn how to use this knowledge to describe data and make informed decisions based on well reasoned statistical arguments. The course elements learnt include: descriptive statistics, inferential statistics, hypothesis development and testing, selections of appropriate statistical tests, and evaluating statistical results. All the elements enabled us to make inferences about a given population from sample data, to perform statistical analyses and to interpret different results. Thus, all the knowledge gained from the statistics course is applicable in real life situations and will also be useful in solving a variety of analytical problems in our future careers. This text takes a look at the five elements of the business statistical course in detail and evaluates their applicability in day-to-day operations and different careers.

Descriptive statistics

Descriptive statistics are used to describe or summarize data in a meaningful way so that patterns can emerge from the data. Numeric values such as range, standard deviation, mean, mode and median are used to make descriptions about the main characteristics of data in a study. They, however, fail to make conclusions beyond analyzed data or conclude on any hypothesis that had been made about the data (Wasserman, 2004). Descriptive statistics can be applied in a variety of situations. For instance, they can be used to describe findings in business related research, to provide insight on business trends, and to explain deviations from expected levels of performance. Descriptive analysis methods can also be used to explain trends followed by stocks that are traded on a financial market and to explain fluctuations in currency in relation to international trade. The knowledge gained can support a career in the U.S. Census Bureau where descriptive characteristics are used to indicate average household sizes, employment rates, pa-capita income and gender and ethic breakdowns. The methods are also useful for people who conduct market research and offer financial services.

Inferential statistics

Inferential statistics makes use of probabilistic techniques to analyze sample information from a known part of a population to improve knowledge about the unknown whole. More specifically, techniques learnt in inferential statistics allowed us to use samples to make informed generalizations about the populations from which the samples were drawn. Downing and Clark (2010) state that the two methods applied in inferential statistics are the testing of statistical hypotheses and the estimation of parameters. The methods incorporate sampling errors that arise when a sample fails to represent the population perfectly. Inferential statistics are applied in daily managerial decision making, product promotion surveys, marketing and research and competitor analysis. It can also be used in the calculation of the consumer price index… [read more]

Chi-Square Analysis: The History, Development, and Applicability of a Common Statistical Tool Term Paper

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Chi Square

An Overview of Chi-Square Analysis: The History, Development, and Applicability of a Common Statistical Tool

There are many different types of information available in the world, and each type can be utilized in very different and highly specific ways depending on both the form of the information and the needs of those utilizing it. These types of information are, in some perspectives, classified into two broader types of information: quantitative and qualitative. Quantitative information is information the can essentially be boiled down to numeric form, and can arise out of either counting or measurement, leading to discrete or continuous data points that can be further analyzed and manipulated to result in deeper understandings of quantifiable phenomena and events. Qualitative data, on the other hand, cannot be reduced to numbers and must be analyzed through other means. Statistics has developed as a field of mathematics that enables researchers to analyze both quantitative and qualitative information in a way that allows for their comparison and analysis in many different ways.

The Chi-Square analysis is one statistical tool that has been developed as a way of analyzing and manipulating qualitative data. Specifically, the Chi Square method was developed in order to compare categorical data in order to determine what type of relationship existed between different qualitative variables (HWS 2010). A drug trial, for instance, might want to compare the number of people receiving a drug to the rates at which their symptoms improved when compared to another group not taking the drug -- the Chi Square analysis test would be a necessary tool in determining the drug's true efficacy.

There are actually several different types of Chi Square analysis that can be utilized, depending on the needs and scope of the research, but the most common of these is the Pearson's Chi-Square test. Karl Pearson was a scientist, philosopher, and mathematician of some renown both during and after his day, and his development of a specific method for analyzing the goodness of fit of a sample distribution and for testing the independence of certain variables/phenomenon (as in the drug trial example given above) is only one of his contributions to the worlds of science and data analysis (Plackett 1983). In 1900, he began working with the Chair of Zoology at the University College of London who supplied a great deal of data to Pearson at a time when his decade of work in correlation (methods of determining the degree to which separate observations occurred together or specifically in the other's absence, suggesting some relationship) and regression analyses (determining the relationship(s) between two or more independent variables on an independent variable) were culminating into the method…… [read more]

Statistics Teaching Measures Essay

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Teaching Measures of Central Tendency

This paper provides a descriptive narration of Measures of Central Tendency (the mean, the median, the mode, the weighted mean and the distribution shapes) with solved examples to illustrate these measures. As the paper describes, measures of central tendency is a category of descriptive analysis, which uses a single value to describe the central representation of any dataset and thus a useful tool in analysis. Due to the disparities that happen to be in different data sets, the mean or the average by itself may not provide the needed information about the distribution of the data. Therefore, the different measures of central tendency give adequate information concerning the distribution of any data set thus important to understand them.

Teaching Measures of Central Tendency

Measures of central tendency is one of the two categories of descriptive statistics that uses a single value as a central representation of a data set and it is important in statistical analysis as it represents a large set of data using only one value. From this category of description, several methods apply to represent this central part. Among the measures includes mean, median, mode, weighted mean and description shapes. The methods of analysis are crucial in statistical analysis as they give information of any data set of interest.

First, we examine the mean as measure of central tendency. Being the commonly utilized measure, it takes another name as average and it involves calculation of summing up all values in a selected population and then dividing the total sum by the involved number of observations. Depending on the desired mean, sample mean, or population mean, the resulting formula can differ slightly. All the same, the result is a central representation of a data set. For instance, if a data set constitutes the following 5 observations, 2, 7, 4, 9,and 3, then the mean will be obtained by summing up all observations (2 + 7 + 4 + 9 + 3) to obtain a cumulative sum of 25, then dividing this result with the number of observations (Mean = 25/5 = 5). Therefore, the mean of the five observations is equal to five (Donnelly, 2004, p. 46).

The next measure is the weighted mean. Unlike the normal mean or average, which allocates equal weight to all values of the observation, weighted mean gives the flexibility to allocate more weight on certain values of the observation compared to others. For example, considering the scores of a student in three exams, that constitutes the exam having a 50% weight, practical contributing 30% weight while the homework takes the remaining 20% weight. If this student scores 80, 70 and 65 in exam, practical and homework respectively, then the weighted mean of these scores obtainable. This is possible through summing up the products of exam score and its respective weight, then dividing the result by to total sum of the three weights, (weighted mean = ((50*80)+(70*30)+(65*20))/(50+30+20))=74) (Salkind,…… [read more]

Bayesian Methods for Data Analysis in Transcription Networks Term Paper

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¶ … Bayesian method refers to methods on probability and statistics particularly those related to the degree of belief interpretation of probability as opposed to frequency interpretation. In Bayesian statistics, a probability is assigned to a statement, whereas under frequency conditions the hypothesis is tested without this probability. Bayesian method, or probability, may be seen as an extension of logic… [read more]

Direction Attach Term Paper

Term Paper  |  2 pages (888 words)
Bibliography Sources: 2


¶ … prioritized items that I would take with me were I going away on a long tri

Lengthy letters, with photographs attached, from people who are emotionally closest to me, with these letters also containing personal memories, assurances of their love, and advice and encouragement for the future.

My laptop -- fully upgraded to the most secure and most functional program then in existence. It should have the basic capabilities, and ability to access and listen to a wide range of music and movies. I would ascertain, too, that I have long-term subscription to the major academic databases that interest me.

A thorough compendium of global philosophy, from past to present, as well as theories from the social sciences, in particular from sociology.

One of Winget's books, likely "People are idiots and I can prove it" (2009)

An introductory textbook to a wide-ranging spectrum of mathematical and logical disciplines. The one I have in mind is called, "A survey of mathematics with applications" (Angel & Porter, 1997)

Part B. Description of Item

1. The letters: I would request those sentimentally closest to me that they describe their feelings towards me in as best a manner as they can, that they describe events that have happened between us that have positively impacted them, and I would conclude with a request for their impressions of my strongest and weakest points. I would ask them to attach their photographs, and an addendum of specific encouragement and/or advice for the future.

2. The laptop -- I might switch to MEPIS, a program I have read that is more secure and reliable than Windows. I would ascertain that it is virus-free with a rapid Internet connection. I would also sign up for long-term subscription with pertinent online Academic databases; ensure that I have access to reliable music and DVD capabilities and, take along a starters' base of several of my best-loved music CD and DVDs (possibly although not necessarily the latter). I would ensure that I have all computer paraphernalia along with a large supply of printing paper, and several empty notebooks as well as a large supply of pens.

3. "People are idiots and I can prove it" (2009): In a down-to-earth, acerbic tone, Winget shows you exactly where and what you are -- he cuts through all the delusions -- whilst in an unusually commonsensical way he shows you how to see the mess in your life for what it is, and how to straighten it out. This is no self-help book; this is a self-'do' book.

4. The compendium: universal in approach, authoritative and comprehensive, an encyclopedia written in a scholarly manner covering every single…… [read more]

Testing a Critical Element of Research Essay

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¶ … Testing

A critical element of research is determining whether a set of observations are the product of chance or the result of the action on the independent variable on the dependent variable. This approach to knowledge creation and verification engages deductive reasoning in the decision making process. Thus, the essential feature of this process is making the correct decision with reference to what the data are pointing to. To make this process more reliable and valid researcher engage a type of thinking and analysis involving statistical testing called hypothesis testing.

A hypothesis is a conjectured statement or predicted statement of relationship between two variables or more variables. The researcher uses the hypothesis to represent the relationship he anticipates will explain some aspect of the variance in the dependent variable. For the purposes of hypothesis, testing the researcher will usually have a null hypothesis and an alternate hypothesis. The null hypothesis is the hypothesis that is actually tested. It is either accepted or rejected by the researcher based on the test results (Ryan 2004). To accomplish this successfully requires that some decisions be made as to when the relationship exists or does not.

The result of the hypothesis test is considered significant if it is highly unlikely that it could be the product of chance. This is determined using a specific threshold for the rejection of the null hypothesis based on a specific significance level. The significance level for the rejection of the null hypothesis is determined before the test in undertaken.

There are two errors that can be made in hypothesis testing, and they center on the rejection of the null hypothesis. The researcher can reject the null hypothesis when the null hypothesis is true. This type of error is called a type I error and the probability of making this type of error called the alpha level. It therefore stands to reason that the lower the probability that is set for the alpha level, then there is a smaller chance of making a type I error. This also means that a more extreme test value is required to have the result be considered as significant. The other type of error that can be made in hypothesis testing is called the type II error. This is the reverse of the Type I error. As the researcher seeks to ensure that the result is not the product of chance, you increase the possibility of not rejecting the null when the null is actually false. So that the type II error leads, the researcher to determine that there is no effect when there actually was an effect.

Aron, Coups & Aron (2011) identify a five-step procedure for successful hypothesis testing. The first step involves restating the research question as a "research hypothesis and a null hypothesis about the populations" in general the null hypothesis is the opposite of the research hypothesis and states that there is no change, no difference or no effect. Secondly, the characteristics of the comparison distribution… [read more]

Codes Were Labeled Thus for Data Analysis A-Level Coursework

A-Level Coursework  |  4 pages (1,173 words)
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¶ … codes were labeled thus for data analysis. Thus the category of participants who found my work to be highly interesting was coded 1, those who found it somewhat interesting were coded 2; those who found it tedious / boring, I coded 3; whilst those who found it highly disinteresting, I coded 4. I should have coded those whose data was missing (e.g. illegible, absent, or had not responded). 1,673 out of 2,715 participants had failed to complete their surveys (there was partially or utterly incomplete missing data). This made for 61.6% of the survey. The cases that I could, ultimately, rely on were 1,042.

Absolute frequency denotes the number of percentage of those who had responded. For instance 650 participants had responded that they were highly interested. This tells us that my presentation (assuming it was that) must have been highly interesting, or I am popular, or perhaps the participants were in some way or other influenced to vote on my behalf, for almost half of the population had found me highly interesting, altogether the overwhelming majority were at least positively inclined towards my presentation whilst only 89 participants ranged to being somewhat bored to being utterly bored. I might conclude that my presentation was successful. The relative frequency is my converting the absolute frequency into an approximate percentage. So, for instance, I calculate the 650 respondents of Code 1 from the total 2715 (650 / 2,715) or gain my relative frequency. The adjusted frequency allows me to compare the response across the various spectrums (to compare the response of the whole). So, for instance, I see that the majority of participants (62.4%) were highly interested in my work, whilst the lowest group of all (2.7%) loathed it. The cumulative frequency is the number of individuals as you move up the scale. For instance 62.4% of participants (i.e. 650 individuals) responded that they were highly interested, by the time you progress to the category of those who were disinterested you receive 100% cumulative frequency.














(b) the genders are equally balanced in their preference for coke (n=7)

2. Mean: all the scores were added and then divided by the number of scores (i.e. 30 in this case).

Standard error: The sample is never a perfectly accurate reflection of the population. There will always be some error between sample and population and the S.E. measures the average difference that should be expected between one and the other. In this case, the S.E. is low.

Median: List the score in order lowest to highest; the median is the middle score in the list (the 50th percentile). Here 16 is the median.

Mode: the most frequently reported score. # 16.

Sample variance: A sample is always biased to its population (different than it) in some way. Sample variance is measuring the extent to which it differs. In this case it verges 6.21% away from norm.

Sample deviation: The square… [read more]

Online Field Trip Comprised of Visits Essay

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Online field trip comprised of visits to five online locations. Each website was related to the teaching and understanding of mathematics. The contents of the sites included information for teachers, parents and students. Some sites were concerned with the testing of particular skills other focused on providing relevant information to interested persons. The following paragraphs will provide a brief summary of the specific websites.

The first site visited was titled "Illumination: Resources for Teaching Math." This website was well organized and vivid. There were links for activities, lessons, standards and other online math resources. The home page of the site provided easy access to some of the more relevant resources on the site. The material on this site is designed to make, the teaching of math fun and enjoyable in the classroom.

Following the "Illumination" site, the next site visited was the "National Council of Teachers of Mathematics" (NCTM) website. This website was abuzz with a multitude of links and a wealth of information specifically for teachers. The resources and articles on this site focused on teacher development. From conferences to job opportunities, the professional development of the teacher was central to this site.

The website "A Math Dictionary for Kids" by Jenny Eather employed bold, bright attention grabbing colors. The website provided definitions to mathematical concepts at a level that children could easily grasp. Selecting a…… [read more]

Curriculum Design Essay

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Curriculum Design

Mathematics -- Trigonometry


Spiritual Principle: "And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...." -- First Kings, chapter 7, verses 23 and 26

This refers to the importance of studying exact measurements (see note) and utilizing mathematical principles to perform accurate calculations.

Students will apply the basic principles of trigonometry to investigate and explain the characteristics of rational functions. Students will apply these basic principles to understand why trigonometric measurement is necessary based on the limits of geometrical measurement. Students will understand basic principles of ratio, sine, cosine, and tangent. Students will be able to explain how trigonometry might be used in their daily lives. (Why is Trigonometry Important?, 2001).

Suggested Activities and Experiences-

1. Introduction to Trigonometric Principles -- To find relevancy, students need to see why trigonometry was invented and what questions it can answer. In addition, there are different problem solving skills necessary when dealing with trigonometric functions. Break students into groups so that there are at least 4 separate groups. Here is the problem:

You are in a group which is to abseil down a rock face tomorrow. Your task is to estimate the height of the face. You have no measuring instruments. You need to determine the height to know how much rope to take. You cannot take excess rope as you are at the start of a four day exercise and you must not have extra weight with you. Tomorrow morning you will walk the track which will take you to the top of the rock face.

Questions on board to read: What…… [read more]

Students at the End of This Grade Term Paper

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Students at the end of this grade level must be able to investigate and solve step and piecewise functions. This means that they must be able to write absolute value functions as piecewise functions. Piecewise functions that students must be able to explain include domain, range, vertex, axis of symmetry, intercepts, extrema, and points of discontinuity. Students must show the ability to solve absolute value equations and inequalities analytically and graphically.

Standard 2: Students must be able to explore exponential functions. This includes the ability to extend properties of exponents to include all integer exponents. They must also be able to solve exponential equations and inequalities of relative simplicity both analytically and graphically. Students must demonstrate an understanding and ability to use basic exponential functions to model reality.

Standard 3: Students must be able to solve quadratic equations and inequalities in one variable. This involves finding real and complex solutions to mathematical equations by means of processes such as factoring, square roots, and the application of the quadratic formula. They must be able to analyze the nature of roots by means of technology and the discriminant. They must be able to describe their solutions by means of linear inequalities.

Standard 4: Students must be able to explore inverses of functions. This includes a discussion of functions and their inverses, by means of concepts such as one-to-oneness, domain, and range. Students must demonstrate an ability to determine the inverses of linear, quadratic and power functions, including restricted domains. They must also be familiar with the use of graphs to determine functions and their inverses. Composition must be used to verify the relationship between functions and their inverses.

Standards for Grade Level 10

Standard 1: Students must be able to analyze a higher degree of polynomial function graphs. This means that they must be able to graph simple polynomial functions and understand the effects of elements such as degree, lead coefficient, and multiplicity of real zeros on the graph. Students must also be able to determine the symmetry of polynomial functions in terms of their nature as even, odd, or neither. They must also demonstrate an ability to explain polynomial functions by referring to elements such as domain and range, intercepts, zeros, relative and absolute extreme, and end behavior.

Standard 2: Students at the end of this grade level must show an ability to explore and understand logarithmic functions as inverses of exponential functions. This includes the definition and understanding of nth root functions, as well as extending the properties of exponents to include rational exponents. Students must be able to extend the laws of exponents in order to understand and use the properties of logarithms.

Standard 3: Students must be able to penetrate various equations and inequalities by finding real and complex roots of higher degree polynomial equations. They must demonstrate an ability…… [read more]

Pre-Calc Trigonometry Journal

Journal  |  9 pages (2,604 words)
Bibliography Sources: 1+


Modeling Real-World Data with Sinusoidal Functions

The sinusoid which is sometimes referred to as the sine wave referrers to a function of mathematics describing a smooth oscillation that is also repetitive. It usually takes place in pure mathematics and also in physics, electrical engineering and signal processing besides numerous other fields. Its form as a function of time (t) is:… [read more]

Representation in Algebra: A Problem Solving Approach Essay

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Representation in Algebra: A Problem Solving Approach

The need for a solid background in mathematics for high school and college students in the 21st century is well documented (Katz & Barton 2007). A number of emerging career fields in the Age of Information are directly related to mathematical knowledge. For instance, Conaway and Rennolds emphasize that the "With the onset… [read more]

NCTM Process Standards Essay

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¶ … NCTM Process Standards


In my class, problem-solving activities were integrated into every learning unit. Some of the methods deployed included learning how to use fractions in a hands-on fashion. As well as doing standard fraction-related problems on paper, students were asked to make visual representations of fractions and use them to solve word problems.

Learning how to make unit conversions was one of the most useful skills learned by the students. Students were given problems similar to those they might cope with in daily life, such as converting standard measurements to the metric system and vice versa. Students also were given the task of painting an imaginary room, and were asked to scale 'up' the amount of paint it would take to cover the surface area, based upon the previous amount used for the smaller, similarly-shaped room.

Students were given problems involving distance, rate, and time. All of these were intended to show the applications of problem-solving activities in math in 'real life' and teach students that understanding math required more than merely manipulating equations.

Reasoning & proof

For all problems worked on in class or at home, students were required to show how they arrived at their answers. It was not enough to simply get the right answer -- the process had to be demonstrated correctly. Focusing on the process of solving a problem over getting the right answer was stressed, contrary to how mathematics is usually taught. Using a process-based teaching strategy underlines the fact that there are different, but equally valid ways of arriving at the same answer for a problem, although some methods are more efficient.

Depending on the learning orientation of the student (verbal, visual, spatial, or kinesthetic) some activities proved more effective for certain members of the class than others, so a variety of strategies were used to teach a single concept. For example, one kinesthetic activity entitled "Walk down the line" required the students…… [read more]

Objective Map Essay

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Grade 9

H.S School Curriculum

Lynchburg, VA

Spiritual Principle

To everything there is a season, and a time to every purpose under heaven (KJV Ecclesiastics 3:1-8)

Standard 1: Students will be able to explain the principles of, graph, and solve step and piecewise functions.

They will be able to convert absolute into piecewise functions.

Standard 2: Students will be able to graph and solve exponential functions and use them to model and predict real life scenarios.

Standard 3: Students will be able to solve quadratic equations and inequalities in one variable. Students will be able to determine and graph the inverses of linear, quadratic and power functions, including restricted domains

Suggested Activities and Experiences


Students will list the types of real world experiences that must be measured in terms of functions or rates of change over time, like changes in distance, temperature, and amounts of interest.

Students will find real world examples of piecewise functions in the newspaper and online, such as the rates of change of distance and speed, cell phone plans, and the value of buying in bulk and then graph these scenarios while in class (McClain & Rieves 2010, p.12).

3. The class will be divided into two halves and given transparencies and markers: one half will graph a linear function, the other half a quadratic function. After graphing both on transparences, students will lay the graphs together and see if the final, combined graph demonstrates or is a new type of function (McClain & Rieves 2010, p.11).

Standard 2:

1. Students will use the principles of compound interest to solve real-world investment goals. For example, a student might ask how he or she can save a specific amount of money within a defined time period to meet a life goal. If he or she has the opportunity to invest in a financial instrument yielding a particular amount of…… [read more]

Geometry Manipulative Essay

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Geometry Manipulative

Elementary Geometry Manipulative

Introducing complex math problems can be difficult to introduce to elementary students. Yet, there are many patterns within mathematics that, if explained properly, can be learned by young eager minds. Thus, it is with this in mind that this geometry lesson aims to teach angle relationships to fifth graders.

The math level being explored is that of the fifth grade. This is an old enough age to begin implementing algebraic and geometrical conceits within the curriculum. Within this grade level, there are three major standards presented by the National Council of Teachers of Mathematics (NCTM): multiplicative thinking, equivalence, and computational fluency, (National Council of Teachers of Mathematics 1989). Thus, it is a perfect age for the beginning basics of geometry. Understanding the formula for finding missing degrees of angles seems very simple but needs a clear and concise explanation. Therefore, within this lesson plan, the concept of angles, degrees, and the relationships between parallel lines and their corresponding angles will be introduced alongside the corresponding algebraic strategy for finding missing variables. In working with the unknown variable, x in most cases, students begin to understand equivalence by using x as a factor which completes a specific sequence. For example, it is clear within angles that if you know one degree within a split sector, you can find the other with the knowledge that the two equal 180 degrees. Thus, the known degree plus the unknown (x) will equal 180 degrees. This concept will satisfy the beginning workings of multiplicative thinking, equivalence, and computational fluency. In order for students to grasp this concept they will need to work with the provided handout and their pencils.

After practice with this hand out, students should be able to grasp the geometrical…… [read more]

Framing the Research Problem: Basic Steps Essay

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Framing the Research Problem: Basic Steps

The specific steps undertaken when framing a research problem for a study will vary with the type of discipline, subject area of research, and the level of accuracy demanded of the research. For example, a small exploratory study designed to see if there is a market for a new fitness studio in a suburban area will demand a different level of scrupulosity than a statistical study designed to see if a new drug has dangerous side effects within certain demographic populations. However, broadly speaking, the steps of the research process are as follows (Marketing research, 2009, Quick MBA):

Define the problem

The problem must be framed in a clear question format, and the data the research is attempting to accumulate must provide a reasonable answer to that question. For example 'is there a statistically significant correlation between hours of television watched and a child's BMI (Body Mass Index)' or 'what characteristics do mothers say influence their breakfast cereal choice when shopping for the family' are both examples of research-based questions.

Most research is framed as a null hypothesis: in other words, the research statement is the opposite of what the researcher actually wants to prove. In the case of a study regarding television watching and childhood obesity, the null hypothesis might state that there is no correlation between hours of television the child watches and the likelihood that the child's BMI will be in the overweight or obese range. The null hypothesis often states conventional wisdom or the status of the control group.

Step 2: Determine research design

Is the research merely designed to describe a specific phenomenon, such as the average age or weight of a consumer of fast food, in the form of descriptive research? Or is it designed to explore possible reasons for the statistical tendency and take the form of exploratory research? Exploratory research might follow a particular population for a period of time to suggest a correlation, such as between obesity and number of fast food restaurants located near a child's school. A causal research design that aims to show a clear cause-and-effect relationship demands a more narrow study design, and usually a control group. It strives to eliminate other possible variables that could influence the outcome: for example, children who live in areas with many fast food establishments near their school might have less access to other leisure-time pursuits because of poverty and a poor diet at home -- factors beyond the location of fast food restaurants might be more of a cause, rather than the availability of fast food alone. More fast food restaurants…… [read more]

Healthcare Practitioners as Well as Other Professionals Essay

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Healthcare practitioners as well as other professionals must know how to deal with statistical data in order to do their jobs on a daily basis. As Rumsey (2003) points out, professionals are presented with statistical data and claims constantly and they must be able to understand how such claims are formulated and whether they are accurate in order to decide what to do about the information presented in such claims. This brief paper will outline some of the most important factors that professionals must understand and apply in order to make practical use of statistics in their work obligations.

Perhaps the first and most important information a professional must have about statistical claims is how the data was gathered and what methodologies were used to crunch the numbers. While the practitioner doesn't necessarily need to know how data was coded or what formulas were used in order to analyze results, a basic understanding of both factors will help the practitioner see if there any red flags in the data. For example, claims that are made about etiology of diseases should be performed under controlled conditions with suitably large and varied populations to ensure that the data is accurate. A study that relies on self-reporting of symptoms in the form of a survey may be adequate for an exploratory study, but not for making determinations about scientific bases for disease or treatment. Therefore the practitioner must understand the difference between quantitative and qualitative research and must know that quantitative research, when conducted with appropriate controls and adequate methodologies can make stronger claims about causal factors.

Rumsey points out the most important statistical measures the practitioner must understand and apply…… [read more]

Geometry Proof Research Proposal

Research Proposal  |  5 pages (1,680 words)
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Geometry Proof

Geometry as a subject learned in school has a primary purpose, and that is to improve the ability of students to reason logically. Logical reasoning is one of the most vital things that a student can learn, not only for mathematics, but for many of the issues that he or she will face in life (Discovering, 2009). Without… [read more]

Psychological Research "It Is Difficult to Turn Thesis

Thesis  |  6 pages (1,904 words)
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¶ … Psychological Research

"It is difficult to turn the pages of a newspaper without coming across a story that makes an important claim about human nature" (America Psychological Association, 2003, par. 1).

Often, we come across specific claims about individual behavior, nature, principles, and/or dynamics which we might find interesting. These articles often cite research studies conducted on the… [read more]

Size in the Field of Statistics Thesis

Thesis  |  2 pages (758 words)
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¶ … Size

In the field of statistics, the term effect size is used to refer to the degree of relationship between two variables. Quite simply, it is the size of the effect that one thing has on another. There are many different examples of effect size that we encounter in our daily lives; it is a comparison and judgment we are so used to main that it appears like second nature. Think about the last time you saw a commercial for a product that advertised itself as "30% more effective than the leading brand," or made some similar "more-than" claim. This is a very direct and open use of effect size -- or at least claimed effect size -- to make what the advertisers want you to believe is a mathematical point. They are basically saying that their product, whatever it is, has a bugger effect size on whatever that products is intended to do. For instance, if a commercial for Brand X weight-gain powder for body builders claimed it was 20% more effective than Brand Y, they would be saying that their powder makes your muscles grow 20% more than the other powder -- that their powder has a larger effect size on muscles.

Though understanding effect size is relatively simple, understanding the mathematical formula behind it can be a little trickier. There are actually many different ways to measure effect size, some of them more reliable for certain cases than others. In general, effect size applies to the meta-analysis aspects of statistics. This means it is used to analyze the analysis, in a way -- while other data is analyzed to establish a correlation, effect size is used to measure the strength or degree of that correlation -- or rather, effect size is the measure of that correlation. According to Professor Becker's overview of effect size on the University of Colorado website (2000), one of the most commonly used measures of effect size is Cohen's d (section II). The "d" stands for difference, and this measure is used to measure effect size between two independent groups of data points. The formula for calculating Cohen's d is (M1-M2)/s, where M1 is the mean of the first set of data points, M2 is the mean of the second…… [read more]

Algebra in Daily Life it Strange Essay

Essay  |  2 pages (718 words)
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Algebra in Daily Life

It strange, though kind of comforting, to think of the many things in our lives that math in general and algebra specifically are so involved in. Strange because we don't often have to do the mathematical operations involved in order to do our daily tasks and go through our routine, and comforting because the concrete and unchanging nature of numbers adds some certainty to this world that can so often seem chaotic and entirely ungrounded. Even if algebra can't predict what will happen to oil prices and mortgage meltdowns, it can at lest provide us with an explanation of what's happening and how it's happening -- and maybe even why.

I will leave this kind of math to the economists and the members of the Federal Reserve board, however; I have neither the know-how nor the inclination to become involved in that mountain of numbers. Still, there are plenty of smaller ways in which numbers play a role in my every day life. One of those ways is my bicycle. I ride my bicycle almost everywhere, and several times I have had minor breakdowns on the road. These incidents have given me a basic understanding of the way my bike and its various gears move me around, and the functions of the bike and its gears can be expressed algebraically. The actual equations that describe the bike's travel would be quite complex and would require a great deal of measurement and experimentation, but the basic equations that would be needed to calculate effort, speed, and travel time for various distances in various gears can be simulated in a simple thought experiment, using simple numbers.

First, a basic description of the bike is needed. I own a twenty-one sped mountain bike, but around town I'm usually on my three-speed cruiser, and for the sake of simplicity, let's look at the equations pertaining to that bike. Terms that need defining in terms of assigning numerical value are the tire circumference (which is also the distance traveled per revolution of the tire), number of revolutions of the tire that result from each turn of the pedals, and effort…… [read more]

Group Spending Comparison Between British, German, French Term Paper

Term Paper  |  5 pages (1,291 words)
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Group Spending Comparison Between British, German, French, And Italian Consumers

From the results, we conclude that the Germans, French, and Italians outspend the British in groups, but that the variance is higher amongst Germans. This is shown by the higher upper limit amongst Germans as compared to others. Germans have the highest standard deviation and standard error, which shows that there is more variance than amongst other nationalities. Since the means fall near the median, we can say that our sample of mean are true.

Task 1(b) - Individual Spending






Sample Standard Deviation

Standard Error

Estimate of Mean

Upper Limit

Lower Limit

Comments: The French and Italians have the highest mean, while the British and the Germans are close together in with a lower spending per person. The variances, however, between the British and the Germans are much higher for the Germans, indicating that there may be a subset of higher spenders. The same is true for the French, which could mean a skew on the higher or lower spending range. This difference between Germans and Brits is supported by the higher limit number for Germans. The French and Italians seem to uniformly spend more, as evidenced by their mid-sized SD and relatively high lower limit and relatively low upper limit. The sample data from the Germans is higher, as shown by the higher standard deviation.

Task 1- - Difference in Means of Group Spending

Group Spending






Sample SD

Comments: as we can analyse from the given results that value of z-score lies within the +/- standard deviation for all the values, which means that the null hypothesis level is accepted for the pair which lie in the 95% of confidence limit.

Task 1(d) - Difference in Means of Individual Spending

Group Spending





Sample SD

Standard Error


















Comments: The above results demonstrate that the Z-score values are above SD for all but FI, BI, BF and BG. For these, the null hypothesis is not proven, for all others the null hypothesis is accepted at a 95% confidence limit.

Task 1(e) - Regression

Comments: Above result of regression shows that if none of the nationality go to the holiday so the expenditure for the respective family will be 515.80,550.69,545.70 and 617.42 for respective nationalities as given in the table. And if they go to the holiday so the expenditure to a large extend will be influenced by the slope of the regression equation.

Task 1(f) - Correlation

Comments: As R-square coefficient shows that,71%, 71%, 66% and 67% of the variation may be predicted by change in actual family size, for respective nationalities and the rest of the percentage i.e,29%, 29%, 34% and 33% are unpredicted. The value of the T-statistics of intercept and slope, indicates that they cannot be zero, and for the each nationality the regression equation can be… [read more]

Ethnomathematics: Mathematics and Culture Term Paper

Term Paper  |  2 pages (741 words)
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What is "ethnomathematics," and what role should the study of indigenous counting systems play in the teaching of number and numeration?

Ethnomathematics, as its name suggests, is the study of the interaction between mathematics and culture. Ethnomathematics' most obvious application in elementary school classes may be in social studies units. Students can study how the development of different mathematical methods enabled the construction of various architectural structures that changed the way people lived and worshipped, like the pyramids. Also, the study of mathematics can be integrated into the study of history, as the development of Arabic numbers facilitated the creation of algebra. Mathematics classes may make use of word problems involving students of many ethnic backgrounds or include units such as examining the concept of slope in the designs of Navajo blankets, a technique used by one teacher in his curriculum (Fugit & Smith, 1995)

However, the application of ethnomathematics can be much broader. "Ethnomathematics is the study of mathematical techniques used by identifiable cultural groups in understanding, explaining, and managing problems and activities arising in their own environment" (Patterson, 2005). For example, the manner in which "professional basketball players estimate angles and distances differs greatly from the corresponding manner used by truck drivers. Both professional basketball players and truck drivers are identifiable cultural groups that use mathematics in their daily work. They have their own language and specific ways of obtaining these estimates and ethnomathematicians study their techniques" (Patterson, 2005).Likewise, the practical physics used by engineers is quite different from the theoretical physics explored by physicists in academia. Although ethnomathematics' use of indigenous counting techniques is often assumed to be non-Western in style, indigenous subgroups within Western society also exist. Approaching math from this practical perspective also provides a very concrete answer to the frequent complaint of many children that math has no application to 'real' life.

The importance of ethnomathematics is perhaps best illustrated by examining the origins of the word more closely. Broken down, the word "ethno" refers culture, and culture refers to national as well as a tribal status, professional status, and even age, in deference to Piaget's exploration of how children of various ages have different perceptions of depth and mass (Patterson, 2005). Culture…… [read more]

Browse the PA State Standards and Select Term Paper

Term Paper  |  4 pages (1,268 words)
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Browse the PA state standards and select the standards on which you would like to base your unit. In a separate document, write two to three paragraphs explaining how your unit of instruction supports local guidelines and student academic content standards. Remember to submit this with your task.


Construct figures incorporating perpendicular and parallel lines, the perpendicular bisector of a line segment and an angle bisector using computer software.

Draw, label, measure and list the properties of complementary, supplementary and vertical angles.

Classify familiar polygons as regular or irregular up to a decagon.

Identify, name, draw and list all properties of squares, cubes, pyramids, parallelograms, quadrilaterals, trapezoids, polygons, rectangles, rhombi, circles, spheres, triangles, prisms and cylinders.

Construct parallel lines, draw a transversal and measure and compare angles formed (e.g., alternate interior and exterior angles).

The standard that I wish to base my unit is on the standards that apply for geometry for grade 8 mathematics. Geometry is one of the most crucial components for the 8th grade level because it supports understanding of higher mathematics at the high school level. Not only is it a very basic component of understanding calculus and linear algebra, but it is the fundamental basis for most science and computer technology classes as well.

The unit that I will create focuses on exploring the properties of the polygon. The polygon has many unique properties and it is a very important unit because it shows students that the squares, rectangles and even circles that they are so familiar with fits within the framework of a greater geometrical understanding, polygons. This essentially ties together all of the random "shapes" that they have had to master into a unified rule for application. According to Pennsylvania standards students need to be able to perform five different functions for polygons, they have to be able to classify polygons as regular or irregular up to the decagon. Identify, name and draw the properties of many different polygons. The unit that I will construct focuses on teaching students the tools necessary for constructing and understanding the properties of polygons. It shows the universality of these shapes and how they can be constructed in accordance with their specific characteristics. My focus will be on understanding the "universal" application of polygons and then applying them to specific shapes so that students do not engage in "memorization" so much as understanding of the root concept of polygons.

My unit fits specifically into the purpose of the PA standards for 8th grade math, and specifically attacks the need for students to have strong geometry experience going into high school. Therefore this unit is critical for the success of students in general and especially when focusing in core understanding.

B. Write four instructional goals for your unit (two for each lesson plan). Enter the goals in the Objectives field in the Unit and Lesson Builder templates.

Unit: Understanding the properties of a polygon (Geometry)

Lesson Plans:

Focus on polygons


Understand what makes an object a… [read more]

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