Question

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.

Answer 1

In statistics, if two groups of numbers have the same mean, their standard deviations, medians, and modes are not necessarily equal.

Step-by-step explanation:

In statistics, if two groups of numbers have the same mean, it does not necessarily mean that their standard deviations, medians, or modes are equal. The correct answer is option d. Other measures of location need not be the same.

Answer 2

d. other measures of location need not be the same.

Step-by-step explanation:

The mean is a measure of central tendency, which is the sum of all the data in the group divided by the total number of data in the group. If two groups of numbers have the same mean, it does not necessarily imply that their mode, median or standard deviation would be the same. Because one group might be much more dispersed/scattered than the other and still have the same mean, also the distribution of numbers in the two groups might be different resulting in different standard deviation, mean and mode for the two groups.