Which of the following summaries are changed by adding a constant to each data value?
I. the mean
II. the median
III. the standard deviation
A) I and III
B) I, II, and III
C) I only
D) I and II
E) III only

Question

Quizplus · Accepted Answer

Adding a constant to each data value will shift the entire data set to the right or left but will not change the relative order of the values, so the median will also be shifted by the same constant. However, the standard deviation measures the spread of the data set around the mean, so adding a constant to each value will also add the same constant to the mean, increasing the distance of each value from the mean and therefore increasing the standard deviation.

Which of the Following Summaries Are Changed by Adding a Constant