What happens to the mean if all values in a data set are increased by 5?

When all values in a data set are increased by a constant, such as 5 in this case, the mean will also increase by that same constant. This is due to the way the mean is calculated: it is the sum of all the values in the data set divided by the number of values.

When each value in the data set is increased by 5, the total sum of the values increases as well. Specifically, if the original mean was calculated as the sum of the original values divided by their count, increasing each value by 5 means that the new sum will be equal to the original sum plus 5 times the number of values. Therefore, when calculating the new mean, this increase will directly translate to an increase of 5 in the mean.

This principle shows that the mean shifts along the number line in direct correlation with changes made to the individual data points. Thus, if every member of the data set increases by a specific amount, the mean follows suit, leading to the conclusion that the mean increases by 5.