Suppose that the average annual salary for city employees is $36,000 with an SD of $12,000. The city council decides to give everyone a raise of $400 per year. What is the new average salary and the new SD?

Mean increases $400 and SD stays the same, because all the scores still have the same relationship to the mean.

To find the new average salary after the raise, simply add the amount of the raise ($400) to the previous average salary ($36,000).

New average salary = $36,000 + $400 = $36,400

To find the new standard deviation (SD), we need to recognize that the raise of $400 per year is applied to every city employee. Since the raise amount is the same for everyone, it does not affect the variability within the data. Therefore, the SD remains unchanged.

New SD = $12,000