The two dot plots below compare the forearm lengths of two groups of schoolchildren:

Two dot plots are shown one below the other. The title for the top dot plot is Forearm Length, Group A and the title for the bottom plot is Forearm Length, Group B. Below the line for each dot plot is written Length in inches. There are markings from 10 to 13 on each line at intervals of one. For the top line there are 4 dots above the first mark, 4 dots above the second mark, and 2 dots above the third mark. For the bottom line there are 2 dots above the second mark, 3 dots above the third mark, and 5 dots above the fourth mark.

Based on visual inspection of the dot plots, which group appears to have the longer average forearm length?

A. Group B, because five children have a forearm length longer than 12 inches.
B. Group B, because a child in the group has the least forearm length of 10 inches.
C. Group A, because no child in the group has a forearm length longer than 12 inches.
D. Group A, because four children in the group have the least forearm length of 10 inches.

It can be seen that more children in group B have forearm length more than 12 inches and there are no children who have forearm length greater than 12 inches in group A.
So, based on the visual inspection of the dot plots, group A, appears to have longer average forearm length.
In order to verify the claim let us find the mean

Mean of Group A

[tex]\dfrac{10\times 4+11\times 4+12\times 2}{10}=10.8\ \text{inches}[/tex]

Mean of Group B

[tex]\dfrac{11\times 2+12\times 3+13\times 5}{10}=12.3\ \text{inches}[/tex]

So, group A has shorter average forearm length.

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