If two groups of numbers have the same mean, then
A) their standard deviations must also be equal.
B) their medians must also be equal.
C) their modes must also be equal.
D) other measures of location need not be the same.

Question

Quizplus · Accepted Answer

The mean measures the center of the distribution, but other measures of location (such as median and mode) only measure the position of certain values within the distribution. Therefore, two groups of numbers with the same mean could have different medians, modes, and other measures of location. Only the standard deviation would have to be equal if the means were equal, as standard deviation measures the variability or spread of the distribution.

If Two Groups of Numbers Have the Same Mean, Then