Which of the following assertions are $\textbf{CORRECT}$?
- Adding $7$ to each entry in a list adds $7$ to the mean of the list.
- Adding $7$ to each entry in a list adds $7$ to the standard deviation of the list.
- Doubling each entry in a list doubles the mean of the list.
- Doubling each entry in a list leaves the standard deviation of the list unchanged.
- $P,Q$
- $Q,R$
- $P,R$
- $R,S$