Question

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 followed by inches in parentheses. There are markings from 9 to 12 on each line at intervals of one. For the top line there are 3 dots above the second mark, 4 dots above the third mark and 3 dots above the fourth mark. For the bottom line there are 3 dots above the first mark, 5 dots above the second mark, and 2 dots above the third mark.

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

Group A, because seven children have a forearm length longer than 10 inches
Group B, because two children have a forearm length longer than 10 inches
Group A, because one child in the group has the least forearm length of 9 inches
Group B, because three children in the group have the least forearm length of 9 inches

Answer 1

According to given text data

Average of both groups

A:-

• 10(3)+11(4)+12(3)/10
• 30+44+36/10
• 66+44/10
• 110/10
• 11

B:-

• 9(3)+5(10)+11(2)/10
• 27+50+22/10
• 49+50/10
• 99/10
• 9.9

Group A has bigger average

Answer 2

Group A, because seven children have a forearm length longer than 10 inches

Explanation:

Create the dot plots based on the given information (please see attached images).

Group A = blue dots

Group B = red dots

From inspection of the attached dot plots, we can see that Group A appears to have the longer average forearm length. This is because 7 children have a forearm length of longer than 10 inches.

To calculate the average forearm length, sum all data values and divide by the total number of data values.

`\textsf{Average of Group A}=( 3 * 10 + 4 * 11 + 3 * 12)/(10)=11`

`\textsf{Average of Group B}=( 3 * 9 + 5* 10+ 2* 11)/(10)=9.9`

Thus proving that Group A has the longer average former length.