The mean and variance of six observations are $8$ and $16$ respectively. If each observation is multiplied by $3$,then the new variance of the resulting observations is:

If each of given $n$ observations is multiplied by a certain positive number $k$,then for the new set of observations -

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 standard deviation of $a, a+d, a+2 d, \ldots, a+2 n d$ is

The mean and variance of six observations are $6$ and $12$ respectively. If each observation is multiplied by $3$,then the new variance of the resulting observations 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 $.69$)