Which of the following assertions are $\textbf{CORRECT}$?

1. Adding $7$ to each entry in a list adds $7$ to the mean of the list.
2. Adding $7$ to each entry in a list adds $7$ to the standard deviation of the list.
3. Doubling each entry in a list doubles the mean of the list.
4. Doubling each entry in a list leaves the standard deviation of the list unchanged.

1. $P,Q$
2. $Q,R$
3. $P,R$
4. $R,S$