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.

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:

[tex]Average=\dfrac{65+67+77+79+88+90+92\times 2+100+102\times 2+109+110+112\times 2+122+136+139}{18}\\\\\\Average=\dfrac{1794}{18}\\\\Average=99.66[/tex]

Similarly for Group B we have:

[tex]Average=\dfrac{50\times 2+55+61+70\times 2+80\times 2+89\times 2+95+100\times 3+110+114}{16}\\\\\\Average=\dfrac{1313}{16}\\\\Average=82.0625[/tex]

Hence, Group A has a greater average time.