Suppose that everyone in a company receives an annual pay raises of 5%. How does it affect the standard deviation of annual pay?

the standard deviation should also increase by 5%

Explanation:

If all the wages had increased by a fixed amount, then the mean would have increased by a fixed amount and the standard deviation would remain the same. e. g. data = 2,4,6 with a mean of 4 and a standard deviation of 1.33. If you add 4 to all the numbers: 6,8,10, you get a new mean of 8, but the standard deviation remains at 1.33

But if you increase all the wages by 5%, some wages will increase a little (the lowest) and others will increase a lot (the highest). If the same set of numbers is increased by 50%: 3,6,9 with a mean of 6 (mean increased by 50%) and a standard deviation of (|3 - 6| + |6 - 6| + |9 - 6|) / 3 = (3 + 0 + 3) / 3 = 2, which is 50% higher