Statistics question bank (Mathematics)

The mean and the standard deviation of 10 observations are 20 and 2 respectively. Each of these 10 observations is multiplied by p and then reduced by $q$, where $p \neq 0$ and $q \neq 0$. If the new mean and new standard deviation (s.d.) become half of the original values, then q is equal to

If both mean and variance of 50 observations $x_1, x_2, \ldots, x_{50}$ are equal to 16 and 256 respectively, then mean of $\left(x_1-5\right)^2,\left(x_2-5\right)^2, \ldots \ldots,\left(x_{50}-5\right)^2$ is