Chapter 12

Chapter 12 - Chapter 12 Describing Distributions with...

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Chapter 12 Describing Distributions with Numbers In this chapter Measures of central tendency Measures of dispersion Measures of position Box-and-whisker plot Measures of central tendency In this chapter we will mainly deal with the calculation of statistics. Remember a statistic is a numerical characteristic of a sample. These are descriptive statistics since they will summarize the data in the sample. A measure of central tendency is a measure of average or typical value. The three measures of central tendency we will look at are the mean, median, and mode. sample mean: When most people use the word average, they are talking about the mean. n x X = where X is the sample mean is the sum x is the data values n is the sample size The mean is the sum of the data values divided by the sample size. Example 1 Select 4 students and ask “how many brothers and sisters do you have?” Suppose the sample yields the following Data: 2,3,1,3 Calculate the mean. Do you think the mean is a good measure of center for this data? Example 2 Suppose we had selected a 5 th person for our sample which had 10 siblings. New Data: 2,3,1,3,10 Calculate the mean. Do you think the mean is a good measure of center for this data? Important characteristics of the mean are below: X is sensitive to extreme scores X is not necessarily a possible value
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An applied example of the mean not being used when extreme values are present is income. If you hear anyone talk about average income, they should say median income. The median is a much better measure for center in this case than the mean. Consider if I wanted to estimate average income for this class. If Bill Gates (a super rich guy) was in the class, what effect would that have on the average? It would make it very high and not a good measure for a typical value. sample median: the middle score Procedure for calculating X ~ (denotes the sample median) follows: rank data from smallest to largest if n is odd, median is the middle score if n is even, median is the average of two middle scores Example 3 Back to number of siblings Data: 2,3,1,3 Solve for the median. Example 4 New Data: 2,3,1,3,10 Solve for the median. Important characteristics of the median are below: X ~ is not sensitive to extreme scores exactly half of the data is below X ~ and exactly half of the data is above X ~ Because of the characteristics of the mean and median, if extreme scores exist in a data set the median is a better measure of central tendency. If extreme scores are unlikely, the mean varies less from sample to sample than the median and is a better measure. sample mode: the most frequent score Example 5 Data: 2,3,1,3 New Data: 2,3,1,3,10 Calculate the mode for the above data sets. There are some major weaknesses with the mode. For example suppose that in the New
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This note was uploaded on 07/12/2011 for the course STATS 200 taught by Professor Bradley,w during the Fall '10 term at KCTCS.

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Chapter 12 - Chapter 12 Describing Distributions with...

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