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Chapter 3

# Chapter 3 - KVANLI PAVUR KEELING Chapter 3 Click to edit...

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Click to edit Master subtitle style 3/10/11 Chapter 3 Data Summary Using Descriptive Measures KVANLI PAVUR KEELING

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3/10/11 Chapter Objectives At the completion of this chapter, you should be able to define and use the following measures: ∙ Measures of Central Tendency: Mean, Median, Mode and Midrange ∙ Measures of Variation: Range, Standard Deviation, Variance,
3/10/11 Chapter Objectives - Continued At the completion of this chapter, you should be able to define and use the following measures: ∙ Measures of Position: Percentiles, Quartiles, and z-scores ∙ Measures of Shape: Skewness

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3/10/11 Summarizing a Sample Chapter 2 described a sample using a graph or chart This chapter summarizes a sample by crunching a number or two, such as an average We refer to these number as descriptive measures There are four different types of
3/10/11 Descriptive Measures There are measures of: • central tendency • variation • position • shape Consider a sample consisting of the number of purchased textbooks this semester for 5 randomly selected students The sample values are {6, 9, 7, 23, 5}

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3/10/11 Measures of Central Tendency These are: • mean • median • midrange • mode These determine where the “middle” of the sample is; that is, a “typical” value The mode is that value that occurs the most often
3/10/11 The Sample Mean The sample mean is the sample average Our sample: {6, 9, 7, 23, 5} The sample mean is books The symbol for the sample mean is 0 . 10 5 5 23 7 9 6 = + + + + X X Read as “x bar”

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3/10/11 The Sample Median To find the median, you must first put the values in order from smallest to largest For our sample, this would be {5, 6, 7, 9, 23} When n is odd, the median is the value in the middle of the ordered data The symbol for the median is Md th n + 2 1 Here, this would be the 3rd value
3/10/11 The Sample Median – n is Even Consider this sample: {2, 4, 8, 12, 16, 18} (n = 6) When n is even, the median is the average of the middle two values Here, Md = books 10 2 12 8 = + th n 2

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3/10/11 The Sample Midrange The midrange is the average of lowest (L) and highest (H) sample values The symbol for the midrange is Mr Mr = The textbook sample is {6, 9, 7, 2 H L + 14 2 23 5 = + This is H This is L
3/10/11 The Sample Mode The mode is that value that occurs the most often in the sample For the textbook example, there is no mode since there are no repeat values If there is a 2-way tie, you state that the modes are ____ and ____ For continuous data, don’t bother

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3/10/11 More on the Sample Mode If your company manufactures clothing, the sample mode is more likely to be of interest rather than the other three measures of central tendency Example: You company manufactures hats The statistic of interest in a sample of head sizes would be the most popular head size since we should manufacture more hats of that size The mean (say, 6.82) would be of little
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Chapter 3 - KVANLI PAVUR KEELING Chapter 3 Click to edit...

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