The $S.D.$ of $15$ items is $6$. If each item is decreased or increased by $1$,then the standard deviation will be:

If the total number of observations is $n = 20$,$\sum x_i = 1000$ and $\sum x_i^2 = 84000$,then the variance of the distribution is

The variance of $50$ observations is $7$. Suppose that each observation in this data is multiplied by $6$ and then $5$ is subtracted from it. Then the variance of that new data is

For the following frequency distribution,find the variance:

$X$	$5$	$6$	$7$	$8$	$10$
Frequency	$3$	$7$	$4$	$2$	$4$

If the coefficient of variation and standard deviation are $ 60 $ and $ 21 $ respectively,the arithmetic mean of the distribution is:

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 $\text{ mm}$)