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

Let the original list of values be $x_1, x_2, \dots, x_n$ with mean $\mu$ and standard deviation $\sigma$.

1. Assertion P: If each entry $x_i$ becomes $x_i + 7$, the new mean is:

   $$\mu_{\text{new}} = \frac{1}{n} \sum (x_i + 7) = \mu + 7$$

   Hence, P is correct.

2. Assertion Q: Standard deviation is invariant under a constant shift (change of origin). The new standard deviation remains $\sigma$, not $\sigma + 7$. Hence, Q is incorrect.

3. Assertion R: If each entry $x_i$ becomes $2x_i$, the new mean is:

   $$\mu_{\text{new}} = \frac{1}{n} \sum (2x_i) = 2\mu$$

   Hence, R is correct.

4. Assertion S: If each entry is scaled by a factor of 2, the standard deviation is also multiplied by 2 (i.e., $\sigma_{\text{new}} = 2\sigma$). Hence, S is incorrect.

Therefore, the correct assertions are P and R, which corresponds to option (C).