Question

A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If 5 were to be added to each score, which of these three statistics would change?

• A. The mean only
• B. The median only
• C. The standard deviation only
• D. The mean and the median
• E. The mean and the standard deviation

Hint:

Adding or subtracting a constant from all data points shifts the mean but does not affect the standard deviation.

Answer 1

The Correct Option is A

Step 1: Effect on the mean.
When a constant is added to all scores, the mean increases by that constant. Thus, the mean will change.
Step 2: Effect on the median.
Adding a constant to all scores will also shift the median by the same constant, but it does not affect the relative ordering of the data, so the median remains unchanged.
Step 3: Effect on the standard deviation.
The standard deviation measures the spread of the data. Adding a constant to each score does not affect the spread, so the standard deviation remains unchanged. \[ \boxed{\text{The mean only}} \]