Which of the following assertions are $\textbf{CORRECT}$?
- $P:$ Adding $7$ to each entry in a list adds $7$ to 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
- $P, Q$
- $Q, R$
- $P, R$
- $R, S$