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

The mean and variance of seven observations are 8 and 16 respectively. If 5 of the observations are $2,4,10,12,14$, then the square root of product of remaining two observations is

The variance of first 50 even natural numbers is

A student scores the following marks in five tests : $54,45,41,43,57$. His score is not known for the sixth test. If the mean score is 48 in six tests, then the standard deviation of marks in six tests is