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Unformatted text preview: Chapter 5 Describing Distributions Numerically 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 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 arent 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 Example Yankees Scores of last 10 games 2 3 3 5 5 5 6 7 7 10 Remember to order the values if they arent 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 Spread Interquartile Range (IQR) First Quartile (Q1) Larger than about 25% of the data Third Quartile (Q3) Larger than about 75% of the data IQR = Q3 Q1 Center (Middle) 50% of the values Finding Quartiles...
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This note was uploaded on 03/30/2008 for the course STAT 101 taught by Professor Graham during the Spring '08 term at Iowa State.
 Spring '08
 Graham
 Standard Deviation

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