# Essays on "Mathematics / Statistics" | Term Papers 1-40

#### William Gosset …

William Gosset William Sealey Gosset was one of the leading statisticians of his time, particularly with his work on the concept of standard deviation in small samples. His theories which were published under the name of "student" are still used today in both the study of statistics and the practical application. Gosset was born on June 13, 1876, in Canterbury, England to Colonel Frederic Gosset and Agnes Sealy Vidal. Gosset was well educated from the beginning first at Winchester, a prestigious private school, then at New College at Oxford. He received his degree in mathematics in 1897, followed two years later by a degree in chemistry (O'Connor and Robertson). It was the combination of these two fields of study that gave Gosset a career and an opportunity to create his theory. Upon graduation, Gosset was hired as a chemist by the Arthur Guinness and Son Company in Dublin. Working in the brewery, required Gosset to constantly attempt to find the best varieties of barley for use in the production of Guinness. This was a complicated procedure of taking small samples to determine the best quality product. Gosset continuously played around with the results of various samples of barley in order to find ones of the best quality with the highest yields that were capable of adapting to changes in soil and weather conditions. Much of his work was trial and error both in the laboratory and on the farms, but he also spent time with Karl Pearson, a biometrician, in 1906-07, at his Galton Eugenics Laboratory at University College (O'Connor and Robertson). Pearson assisted Gosset with the mathematics of the process. Gosset published his findings under the name of "student" because the brewery would not permit him to publish. The brewery feared that trade secrets would get out if information about the brewing process was published. Consequently, Gosset had to assume a pseudonym even though his information would not have impacted the business in the way the brewery was concerned (O'Connor and Robertson). Gosset published his work in an article called "The Probable Error of a Mean" in a journal operated by Pearson called Biometrika. As a result of Gosset's pseudonym, his contribution to statistics is called the Student t-distribution. Gosset's work caught the attention of Sir Ronald Aylmer Fisher, a statistician and geneticist of the time. Fisher declared that Gosset had developed a "logical revolution" with his findings about…

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#### Guillaume Francois Antoine De L'hopital …

Apparently, out of respect to the mathematician who made much of his fame possible, L'Hopital abandoned the project. 'L'Hopital was a major figure in the early development of the calculus on the continent of Europe" (Robinson 2002). During this time of scientific and mathematic enlightenment in Europe, and particularly in France, L'Hopital established himself as one of the world's premier mathematicians and book writers. It is noteworthy that many of the accomplishments L'Hopital is credited with have come into question over the years. Most obvious among these include the rule that is named after him, which every calculus student has been forced to memorize for the past three hundred years. Despite these questions, perhaps the most telling thing about L'Hopital is that he was widely accepted and respected by his peers. He became the third man on continental Europe to learn calculus simply because he impressed the man who later became his tutor. "According to the testimony of his contemporaries, L'Hopital possessed a very attractive personality, being, among other things, modest and generous, two things which were not widespread among the mathematicians of his time." (Robinson 2002). He died on the second of February, 1704, in Paris; the city of his birth. Works Cited 1. Addison and Wesley. Calculus: Graphical, Numerical, Algebraic. New York: Addison-Wesley Publishing, 1994. 2. Feinberg, Joel and Russ Shafer-Landau. Reason and Responsibility. Boston: Wadsworth Publishing, 1999. 3. Goggin, J. And R. Burkes. Traveling Concepts II: Frame, Meaning and Metaphor. Amsterdam: ASCA Press, 2002. 4. Greenberg, Michael D. Advance Engineering Mathematics: Second Edition. Delaware: University of Delaware, 1998. 5. O'Connor, J.J. And EF Robertson. "Blaise Pascal." JOC/EFR. December 1996. School of Mathematics and Statistics, University of St. Andrews, Scotland.……

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#### Statistics in Research and Analysis the Experiments, …

¶ … 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 USE of STATISTICS in RESEARCH and ANALYSIS This paper concerns itself with the use of statistics as a means and the important tool in research and analysis -- both in…

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#### Art and Mathematics Are Related and That …

¶ … 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…

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#### Mathematics in Digital Photography the …

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. Conclusion 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…

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#### Statistics Are Integral to Research but it …

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……

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#### NCTM's Agenda for Action and Standards …

Mathematics 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……

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#### SPSS Statistics: Social Science Research Instructions: Reading: …

SPSS Statistics: Social Science Research Instructions: 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? 63.317 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……

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#### Actuaries the Jobs Rated Almanac …

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. References 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.…

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#### Statistics: Marketing the Practice Applying One's Knowledge …

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……

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#### Statistics in Management …

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……

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#### Impact of Mathematics on Economics From the Medieval Time …

¶ … 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……

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#### Damned Lies and Statistics by Joel Best …

¶ … 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……

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#### Araybhata's Contributions to Mathematics & Algebra Aryabhata …

ARAYBHATA'S CONTRIBUTIONS to MATHEMATICS & ALGEBRA 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……

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#### Inferential Statistics? What Are the Differences? When …

¶ … 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…

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#### Mathematics Education the Objective of This Work …

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;……

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#### Statistics Being Studied Were the …

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=…

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#### Statistic Project …

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……

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#### How Statistics Apply to Entrepreneurship …

¶ … 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……

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#### Statistics: A Question Unanswered Before There Can …

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…

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#### Statistics Anxiety and Graduate Students in the …

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…

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#### Aesthetic Appeal of Mathematics …

Mathematics 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……

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#### Growth of Mathematics …

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……

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#### Mathematics as a Creative Art …

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……

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#### Inferential Statistics to Evaluate Sample …

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<…

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#### Lie With Statistics Huff, Darrell. …

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…

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#### Chinese Mathematics in Ancient China, …

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

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#### "Basic Statistics for the Behavioral …

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……

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#### Correlation and Regression …

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…

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#### Mathematics for Elementary Educators …

¶ … 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:…

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#### Carl Friedrich Gauss …

Carl Friedrich Gauss This is a template and guideline. Please do not use as a final turn-in paper. Biography 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……

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#### Mathematic v. Conceptual Modeling Limitations of Models …

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……

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#### What's Math Got to Do With it by Jo Boaler …

¶ … 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…

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#### Professional Mathematical Societies …

Mathematics 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…

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#### Statistics Allowable With Nominal, Ordinal and Interval …

¶ … 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…

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#### Blaise Pascal Bio Blaise Pascal's Biography Blaise …

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.…

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#### Statistics for Social Sciences Correlation This Assignment …

Statistics for Social Sciences Correlation 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.……

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#### Neuman (2003), Researchers Frequently Need to Summarize …

¶ … 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…

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#### Aristotle and His Contribution to Mathematics and …

¶ … 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……

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#### George Polya …

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…

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