Essay: Statistics Teaching Measures

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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,… [END OF PREVIEW]

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