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101 Ch. 5

# 101 Ch. 5 - Chapter 5 Describing Distributions Numerically...

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Chapter 5 Describing Distributions Numerically

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Describing the Distribution Center Median Mean Spread Range Interquartile Range Standard Deviation
Median Literally = middle number (data value) n (number of observations) is odd Order the data from smallest to largest Median is the middle number on the list (n+1)/2 number from the smallest value Ex: If n=11, median is the (11+1)/2 = 6 th number from the smallest value Ex: If n=37, median is the (37+1)/2 = 19 th number from the smallest value

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Example – August Temps High Temperatures for Des Moines, Iowa taken from the first 13 days of August 2005. 71 76 81 81 85 86 90 90 91 93 93 96 96 Remember to order the values, if they aren’t already in order! 13 observations (13+1)/2 = 7 th observation from the bottom Median = 90
Median n is even Order the data from smallest to largest Median is the average of the two middle numbers (n+1)/2 will be halfway between these two numbers Ex: If n=10, (10+1)/2 = 5.5, median is average of 5 th and 6 th numbers from smallest value

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Example – Yankees Scores of last 10 games 2 3 3 5 5 5 6 7 7 10 Remember to order the values if they aren’t already in order! 10 observations (10 + 1)/2 = 5.5, average of 5 th and 6 th observations from bottom Median = 5
Spread Range is a very basic measure of spread (Max – Min). It is highly affected by outliers Makes spread appear larger than reality Ex. The annual numbers of deaths from tornadoes in the U.S. from 1990 to 2000: 53 39 39 33 69 30 25 67 130 94 40 Range with outlier: 130 – 25 = 105 Range without outlier: 94 – 25 = 69

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