Chapter 3

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

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Click to edit Master subtitle style 3/13/11 Chapter 3 – Data Summary Using Descriptive Measures KVANLI PAVUR KEELING

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3/13/11 Chapter Objectives v At the completion of this chapter, you should be able to define and use the following four measures: ∙ Measures of Central Tendency: Mean, Median, Mode and Midrange ∙ Measures of Variation: Range, Standard Deviation, Variance, and
3/13/11 Chapter Objectives - Continued v 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 and

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3/13/11 Measures of Central Tendency v 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
3/13/11 Central Tendency Calculation v Example: v Consider a sample consisting of the number of purchased textbooks this semester for 5 randomly selected students v The sample values are {6, 9, 7, 23, 5} Here, the sample size is n = 5

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3/13/11 The Sample Mean v The sample mean is the sample average v Our sample: {6, 9, 7, 23, 5} v The sample mean is books v The symbol for the sample mean is v So, = 10 0 . 10 5 5 23 7 9 6 = + + + + X X Read as “x bar”
3/13/11 The Sample Median v Median (Md) is the center of the ordered array v 2 steps to find the Md. v 1st step: put the values in order from smallest to largest v For our sample, this would be {5, 6, 7, 9, 23} v 2nd step: Consider n is odd or even. th n + 2 1 Here, this would be the 3rd value

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3/13/11 The Sample Median – n is Even v IF n is even , the median is the average of the middle two values Consider this sample: {2, 4, 8, 12, 16, 18} (n = 6) v Here, Md = books v In general for n even, Md is the average of the 10 2 12 8 = + th n 2
3/13/11 The Sample Midrange v The midrange is the average of lowest (L) and highest (H) sample values v The symbol for the midrange is Mr v Mr = v The textbook sample is {6, 9, 7, 23, 5} 2 H L + 14 2 23 5 = + This is H This is L

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3/13/11 The Sample Mode v The mode ( Mo ) is that value that occurs more than once and the most often in the sample. v For the textbook example, there is no mode since there are no repeat values v If there is a 2-way tie, you state that the modes are ____ and ____ v For continuous data, don’t bother looking for a mode
3/13/11 More on the Sample Mode v If your company manufactures clothing , the sample mode is more likely to be of interest rather than the other three measures of central tendency v Example: Your company manufactures hats v 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 v The mean (say, 6.82), median and midrange

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3/13/11 Outlier v In statistics, an outlier is an observation that is numerically distant from the rest of the data.
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