Question

the means and mean absolute deviations of monthly snowfall during the winter months in two cities are shown in the table below.

	north town	south town
mean absolute deviation	0.55 in.	0.48 in.

the difference of the means is found and then compared to each of the mean absolute deviations. which is true?

• the difference between the means is about equal to the mean absolute deviation of the data sets.
• the difference between the mean is about 2 times the mean absolute deviation of the data sets.
• the difference between the mean is about 4 times the mean absolute deviation of the data sets.
• the difference between the means is about 5 times the mean absolute deviation of the data sets.

Explanation:

Step1: Calculate difference of means

$8.9 - 6.3 = 2.6$

Step2: Compare to MAD values

First, take average MAD: $\frac{0.55 + 0.48}{2} = 0.515$
Then find ratio: $\frac{2.6}{0.515} \approx 5$
Or compare to individual MADs: $\frac{2.6}{0.55} \approx 4.7$, $\frac{2.6}{0.48} \approx 5.4$, both close to 5.

Answer:

The difference between the means is about 5 times the mean absolute deviation of the data sets.