Question

The two dot plots below show the heights of some sixth graders and some seventh graders:

Two dot plots are shown one below the other. The title for the top dot plot is Sixth Graders and the title for the bottom plot is Seventh Graders. Below the line for each dot plot is written Height followed by inches in parentheses. There are markings from 52 to 57 on the top line and the bottom line at intervals of one. For the top line there are 2 dots above the first mark, 1 dot above the second mark, 1 dot above the third mark and 2 dots above the fourth mark. For the bottom line, there is 1 dot for the first mark, there are 3 dots above the second mark, 2 dots above the third mark.

The mean absolute deviation (MAD) for the first set of data is 1.2 and the MAD for the second set of data is 0.6. Approximately how many times the variability in the heights of the seventh graders is the variability in the heights of the sixth graders? (Round all values to the tenths place.)

0.3
1.2
1.7
2.0

Answer 1

Answer: 2.0 (choice D)

Reason:

We divide the two mean absolute deviation (MAD) values to get (1.2)/(0.6) = 2.0

The variability in the first set (the 6th graders) is exactly twice that of the variability of the second set (the 7th graders).

The MAD is one measure of variability or spread. Another would be the standard deviation. The larger the value, the more spread out the data points will be.