Question

The dot plot below shows the amount of time two random groups of students took to solve a puzzle:

A dot plot shows Puzzle Solving Time in seconds on the horizontal axis. For Group A, there is 1 dot on 65, 1 dot on 67, 1 dot on 77, 1 dot on 79, 1 dot on 88, 1 dot on 90, 2 dots on 92, 1 dot on 100, 2 dots on 102, 1 dot on 109, 1 dot on 110, 2 dots on 112, 1 dot on 122, 1 dot on 136, and 1 dot on 139. For Group B, there are 2 dots on 50, 1 dot on 55, 1 dot on 61, 2 dots on 70, 2 dots on 80, 2 dots on 89, 1 dot on 95, 3 dots on 100, 1 dot on 110, and 1 dot on 114.
Based on visual inspection of the dot plots, which of the following groups, if any, shows a greater average time required to solve the puzzle?
Group A
Group B
Both groups show about the same average time.
No conclusion about average time can be made from the data.

Answer 1

The answer would be A Group A

Answer 2

Based on the dot plot the group that has a greater average time is:

Group A.

Explanation:

Clearly from the set of values from the dot plot we have that For Group A the dots are assigned to a higher value ( i.e. the range of the values are between 65 to 139) that means that it will result in more average (or mean) whereas in Group B the values are assigned to a lesser value ( as the range is between 50 to 114) and hence will result in a lower mean.

Also , we may calculate mean for each group as:

Group A:

Similarly for Group B we have:

`Average=(50* 2+55+61+70* 2+80* 2+89* 2+95+100* 3+110+114)/(16)\\\\\\Average=(1313)/(16)\\\\Average=82.0625`

Hence, Group A has a greater average time.