If $M.D.$ is $12$,the value of $S.D.$ will be

Let in a series of $2n$ observations,half of them are equal to $a$ and the remaining half are equal to $-a$. Also,by adding a constant $b$ to each of these observations,the mean and standard deviation of the new set become $5$ and $20$,respectively. Then the value of $a^{2} + b^{2}$ is equal to ....... .

The variance of the first $50$ even natural numbers is

Find the mean and variance for the following frequency distribution:

Classes	$0-30$	$30-60$	$60-90$	$90-120$	$120-150$	$150-180$	$180-210$
$f_i$	$2$	$3$	$5$	$10$	$3$	$5$	$2$

The mean of four observations is $3$. If the sum of the squares of these observations is $48$,then their standard deviation is

Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution:

$X_i$	$0$	$1$	$2$	$3$	$4$	$5$
$f_i$	$k+2$	$2k$	$k^2-1$	$k^2-1$	$k^2-1$	$k-3$

where $\sum f_i=62$. If $[x]$ denotes the greatest integer $\leq x$,then $[\mu^2+\sigma^2]$ is equal to: