Calculate the standard deviation of the following data:

$x_i$	$5$	$15$	$25$	$35$	$45$	$55$	$65$	$75$
$f_i$	$5$	$8$	$7$	$12$	$28$	$20$	$10$	$10$

The frequency distribution of population of males in different age groups is given below:

Find the mean deviation about mean.

Can we say that the weights show greater variation than the heights?

The sum and sum of squares corresponding to length $x$ (in $\mathrm{cm}$ ) and weight $y$ (in $\mathrm{gm}$) of $50$ plant products are given below:

$\sum _{\mathrm{i}=1}^{50}{\mathrm{x}}_{\mathrm{i}}=212,\underset{\mathrm{i}=1}{\overset{50}{ \sum }}{\mathrm{x}}_{\mathrm{i}}^2=902.8,\underset{\mathrm{i}=1}{\overset{50}{ \sum }}{\mathrm{y}}_{\mathrm{i}}=261,\underset{\mathrm{i}=1}{\overset{50}{ \sum }}{\mathrm{y}}_{\mathrm{i}}^2=1457.6$

Which is more varying, the length or weight?

Given that $12$ is mean of $10$ observations. $7$ is the variance of $10$ observations $x_1,x_2,x_3,\dots ,x_{10}.$ If each observation is multiplied by $4$ . Find the new variance of the resulting observations.