M07.D-S.2.1.1
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 are 2 dots for the fifth mark, there are 4 dots above the sixth 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 0.4. 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.)
(5 points)
Group of answer choices
3.0
3.2
1.5
0.8
To find the answer, we need to compare the mean absolute deviations (MAD) of the two sets of data. The MAD is a measure of the variability in a data set.
The MAD for the sixth graders is 1.2 and the MAD for the seventh graders is 0.4. To determine how many times the variability in the seventh graders' heights is compared to the sixth graders' heights, we divide the MAD of the seventh graders by the MAD of the sixth graders.
0.4 / 1.2 = 0.333
Rounding to the tenths place, we get approximately 0.3. Therefore, approximately how many times the variability in the heights of the seventh graders is the variability in the heights of the sixth graders is 0.3.
So, the closest answer choice is 0.3, or 3.0 when rounded to a whole number.
Therefore, the answer is:
3.0