The variance of the following distribution is:

Marks	$1-3$	$3-5$	$5-7$	$7-9$
Number of students	$40$	$30$	$20$	$10$

Find the variance of the sequence $a, a + d, a + 2d, \dots, a + 2nd$.

The standard deviation and mean of five observations are $0$ and $9$ respectively. If one of the observations is changed such that the mean of the new set of five observations becomes $10$,then their standard deviation is

The variance of the observations $8, 12, 13, 15, 22$ is:

Consider three observations $a, b,$ and $c$ such that $b = a + c$. If the standard deviation of $a + 2, b + 2, c + 2$ is $d$,then which of the following holds true?

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: