Question

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

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

A. The difference between the means is about equal to the mean absolute deviation of the data sets.

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

C. The difference between the mean is about 4 times the mean absolute deviation of the data sets.

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

Answer 1

Option D.

Explanation:

Given information:

Mean of north town = 8.9 inches

Mean of south town = 6.3 inches

Mean absolute deviation of north town = 0.55 inches.

Mean absolute deviation of south town = 0.48 inches.

The difference of the means of both towns is

`8.9-6.3=2.6`

Let the difference between the means is about k₁ times the mean absolute deviation of the data sets 1 .

`k_1(0.55)=2.6`

`k_1=(2.6)/(0.55)=4.7272..\approx 5`

Let the difference between the means is about k₂ times the mean absolute deviation of the data sets 2 .

`k_2(0.48)=2.6`

`k_2=(2.6)/(0.48)=5.4166..\approx 5`

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

Therefore, the correct option is D.

Answer 2

The correct option is D

Explanation:

From the given table it is clear that the mean of north town is 8.9 inches and the mean of south town be 6.3.

The difference of the means is

`D=8.9-6.3=2.6`

Let the difference between the means is about k times the mean absolute deviation of the data sets.

`k(0.55)=2.6`

`k=(2.6)/(0.55)=4.7272...\approx 5`

`k(0.48)=2.6`

`k=(2.6)/(0.48)=5.4166667\approx 5`

Therefore the difference between the means is about 5 times the mean absolute deviation of the data sets. Hence the correct option is D.