If $S_1$ and $S_2$ are the variances of the first $2k$ and $k$ $(k > 1)$ natural numbers respectively,then $(S_1 / S_2)$ lies in the interval

If the standard deviation of data is $12$ and mean is $72$,then the coefficient of variation is: (in $\%$)

$\text{Assertion (A):}$ Variance of $4x_1, 4x_2, \ldots, 4x_n$ is $16$ times the variance of $x_1, x_2, \ldots, x_n$. $\text{Reason (R):}$ If $y = ax + b$,then variance of $y$ is $a(\text{variance of } x) + b$. The correct option among the following is

The variance of the following frequency distribution is:

Class Interval	$0$-$4$	$4$-$8$	$8$-$12$	$12$-$16$	$16$-$20$
Frequency	$2$	$4$	$6$	$3$	$1$

The standard deviation of the data $6, 7, 8, 9, 10$ is

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 ....... .