Which of the following assertions are CORRECT?

P: Adding 7 to each entry in a list adds 7 to the mean of the list
Q: Ad...

Question

Which of the following assertions are CORRECT?

P: Adding 7 to each entry in a list adds 7 to the mean of the list
Q: Adding 7 to each entry in a list adds 7 to the standard deviation of the list
R: Doubling each entry in a list doubles the mean of the list
S: Doubling each entry in a list leaves the standard deviation of the list unchanged

A. P, Q
B. Q, R
C. P, R
D. Q, S

Accepted Answer

Assertions P and R are correct. Answer: C. P, R Mean is a linear average, so adding a constant shifts it by that constant, and multiplying all values by a constant scales the mean by the same factor. Standard deviation measures spread (distances from the mean). Adding a constant to all values shifts the entire dataset uniformly, so deviations from the mean do not change, leaving SD unchanged. Doubling all values doubles the deviations, so SD is also doubled. Hence P and R are correct; Q and S are both wrong.