Comparing Measures of Center and Variability — Quiz
Question 2 • Grade 7 Mathematics
The means and mean absolute deviations of the individual times of members of two relay swim teams are shown in the table. Means and Mean Absolute Deviations of Individual Times of Members of 4 times 200 –meter Relay Swim Teams Team A Team B Mean 127 point 9 s 127 point 4 s Mean Absolute Deviation 0 point 2 6 s 0 point 2 3 s The difference of the means is found and then compared to each of the mean absolute deviations. Which is true?
Answer
A
The difference between the mean times is about 2 times the mean absolute deviation of the data sets.
B
The difference between the mean times is about equal to the mean absolute deviation of the data sets.
C
The difference between the mean times is about 16 times the mean absolute deviation of the data sets.
D
The difference between the mean times is about 5 times the mean absolute deviation of the data sets.
Explanation
The difference between the team means is 127.9 − 127.4 = 0.5 seconds. Compared with the mean absolute deviations, 0.5 ÷ 0.26 is about 1.9, and 0.5 ÷ 0.23 is about 2.2. So the difference is about 2 times each team’s mean absolute deviation; choice A is correct.
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