The salaries at a small company have a standard deviation of $12,000. If the company owner decides to give every employee a 5% raise, which statement describes the effect on the standard deviation of the salaries?
- The new standard deviation will be 5% greater than $12,000. (correct answer)
- The new standard deviation will still be $12,000.
- The new standard deviation will be $12,000 plus 5% of the mean salary.
- The new standard deviation will increase by $600.
Explanation: A 5% raise means every salary is multiplied by 1.05. When every value in a dataset is multiplied by a positive constant, the standard deviation is also multiplied by that same constant. Therefore, the new standard deviation will be 1.05 times the old standard deviation. This is equivalent to saying it will be 5% greater than $12,000. The change is not a fixed amount like $600 (which is 5% of $12,000), but a multiplicative increase. It does not stay the same as it would if a fixed amount were added to each salary.