For a set of $50$ observations,the sum of their squares is $3050$ and their arithmetic mean is $6$. Find the standard deviation of these observations.

Find the mean and variance for the following frequency distribution.

Classes	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$
Frequencies	$5$	$8$	$15$	$16$	$6$

The mean of $5$ observations is $7$. If four of these observations are $6, 7, 8, 10$ and one is missing,then the variance of all the five observations is:

The variance of $20$ observations is $5$. If each of the observations is multiplied by $2$,then the variance of the resulting observations is:

If the mean and standard deviation of $n$ observations $x_1, x_2, \dots, x_n$ are $\bar{x}$ and $\sigma$ respectively,then what is the sum of the squares of the observations?

The variance of the variates $112, 116, 120, 125, 132$ about their $A.M.$ is