Question

the means and mean absolute deviations of the individual times of members of two relay swim teams are shown in the table below.

	means and mean absolute deviations of individual times of members of 4 x 200 - meter relay swim teams
mean	127.9 s	127.4 s
mean absolute deviation	0.26 s	0.23 s

the difference of the means is found and then compared to each of the mean absolute deviations. which is true?
the difference between the mean times is about equal to the mean absolute deviation of the data sets.
the difference between the mean times is about 2 times the mean absolute deviation of the data sets.
the difference between the mean times is about 5 times the mean absolute deviation of the data sets.
the difference between the mean times is about 16 times the mean absolute deviation of the data sets.

Explanation:

Step1: Calculate the difference of the means

$|127.9 - 127.4|= 0.5$

Step2: Compare with mean - absolute - deviations

Mean absolute deviation of Team A is $0.26$ and of Team B is $0.23$. The average of the mean - absolute - deviations is $\frac{0.26 + 0.23}{2}=\frac{0.49}{2}=0.245$. And $\frac{0.5}{0.245}\approx2$.

Answer:

The difference between the mean times is about 2 times the mean absolute deviation of the data sets.