For the following frequency distribution,the variance is approximately equal to

Class Interval	$0$-$5$	$5$-$10$	$10$-$15$	$15$-$20$	$20$-$25$
Frequency	$4$	$1$	$10$	$3$	$2$

The coefficient of variation and standard deviation of an ungrouped data are $60$ and $21$ respectively. If $15$ is added to every observation of the data,then the coefficient of variation of the new data is

The variance of $20$ observations is $5$. If each observation is multiplied by $3$ and then $8$ is added to each number,then the variance of the resulting observations is:

Let $x_1, x_2, \dots, x_n$ be $n$ observations,$\bar{x}$ be their mean,and $\sigma^2$ be their variance.
Statement-$1$: The variance of $2x_1, 2x_2, \dots, 2x_n$ is $4\sigma^2$.
Statement-$2$: The mean of $2x_1, 2x_2, \dots, 2x_n$ is $4\bar{x}$.

The mean and standard deviation of $100$ items are $50$ and $4$ respectively. The sum of the squares of all the items is:

$5$ students of a class have an average height $150 \, cm$ and variance $18 \, cm^2$. $A$ new student,whose height is $156 \, cm$,joined them. The variance (in $cm^2$) of the height of these $6$ students is