If the mean and variance of the data $65, 68, 58, 44, 48, 45, 60, \alpha, \beta, 60$ where $\alpha > \beta$ are $56$ and $66.2$ respectively,then $\alpha^2 + \beta^2$ is equal to

Let $X = \{x \in \mathbb{N} : 1 \le x \le 19\}$ and for some $a, b \in \mathbb{R}$,$Y = \{ax + b : x \in X\}$. If the mean and variance of the elements of $Y$ are $30$ and $750$,respectively,then the sum of all possible values of $b$ is

The mean and $S.D.$ of $1, 2, 3, 4, 5, 6$ are

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 $\text{ mm}$)

For a frequency distribution,the standard deviation is computed by: