The variance of the variates $112, 116, 120, 125, 132$ about their $A.M.$ is

Find the mean and variance for the following data:

$x_i$	$6$	$10$	$14$	$18$	$24$	$28$	$30$
$f_i$	$2$	$4$	$7$	$12$	$8$	$4$	$3$

The diameters of circles (in mm) drawn in a design are given below:

Diameters	$33-36$	$37-40$	$41-44$	$45-48$	$49-52$
No. of circles	$15$	$17$	$21$	$22$	$25$

Calculate the standard deviation and mean diameter of the circles.
[ Hint : First make the data continuous by making the classes as $32.5-36.5, 36.5-40.5, 40.5-44.5, 44.5-48.5, 48.5-52.5$ and then proceed.] (in $\text{ mm}$)

The variance of $20$ observations is $5$. If each of the observations is multiplied by $2$,then the variance of the resulting observations is:

The standard deviation of the following distribution is:

$C$.$I$.	$0$ - $6$	$6$ - $12$	$12$ - $18$
f_i	$2$	$4$	$6$

The mean and standard deviation of six observations are $8$ and $4,$ respectively. If each observation is multiplied by $3,$ find the new mean and new standard deviation of the resulting observations.