The variance of the ungrouped data $2, 12, 3, 11, 5, 10, 6, 7$ is

The data is obtained in tabular form as follows:

$x_i$	$60$	$61$	$62$	$63$	$64$	$65$	$66$	$67$	$68$
$f_i$	$2$	$1$	$12$	$29$	$25$	$12$	$10$	$4$	$5$

Find the standard deviation of the given data. (in $.69$)

If each observation of a distribution with standard deviation $\sigma$ is increased by $\lambda$,find the variance of the new observations.

The variance of the following data is

$x_{i}$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$
$f_{i}$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$

The arithmetic mean and standard deviation of a data set of nine numbers are $13$ and $5$ respectively. If $3$ is included as the $10^{th}$ item of the data,then the variance of the data set of ten numbers is:

If the mean of $100$ observations is $50$ and their standard deviation is $5$,then the sum of squares of all observations is