EXAMPLE 2 Compare measures of dispersion The top 10 finishing times (in seconds) for runners in two men’s races are given. The times in a 100 meter dash.

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EXAMPLE 2 Compare measures of dispersion The top 10 finishing times (in seconds) for runners in two men’s races are given. The times in a 100 meter dash are in set A, and the times in a 200 meter dash are in set B. Compare the spread of the data for the two sets using (a) the range and (b) the mean absolute deviation. A: 10.62, 10.94, 10.94, 10.98, 11.05, 11.13, 11.15, 11.28, 11.29, RUNNING

EXAMPLE 2 Compare measures of dispersion B: 21.37, 21.40, 22.23, 22.23, 22.34, 22.34, 22.36, 22.60, 22.66, SOLUTION a. A: – B: – = 0.7 = 1.36 The range of set B is greater than the range of set A. So, the data in B cover a wider interval than the data in A. ANSWER

EXAMPLE 2 Compare measures of dispersion b. The mean of set A is 11.07, so the mean absolute deviation is: | – | + | – | + … + | – | 10 = The mean of set B is , so the mean absolute deviation is: | – | + | – | + … + | – | 10 =

EXAMPLE 2 Compare measures of dispersion The mean absolute deviation of set B is greater, so the average variation from the mean is greater for the data in B than for the data in A. ANSWER

GUIDED PRACTICE for Example 2 RUNNING 2. The top 10 finishing times (in seconds) for runners in a men’s 400 meter dash are 46.89, 47.65, 48.15, 49.05, 49.19, 49.50, 49.68, 51.09, 53.31, and Compare the spread of the data with that of set A in Example 2 using (a) the range and (b) the mean absolute deviation. a. The range of finishing times for the men’s 400m dash (6.79) is greater than the range for set A (0.7). ANSWER b. The mean absolute deviation is greater for the men’s 400m dash (1.7246) than it is for set A (0.164).