Let $x_1, x_2, \dots, x_{100}$ be $100$ observations such that $\sum x_i = 0$,$\sum_{1 \le i < j \le 100} |x_i x_j| = 80000$,and the mean deviation from their mean is $5$. Then their standard deviation is:

The sum and sum of squares corresponding to length $x$ (in $cm$) and weight $y$ (in $gm$) of $50$ plant products are given below:
$\sum\limits_{i = 1}^{50} {{x_i} = 212, \sum\limits_{i = 1}^{50} {x_i^2} = 902.8, \sum\limits_{i = 1}^{50} {{y_i} = 261, \sum\limits_{i = 1}^{50} {y_i^2 = 1457.6} } }$
Which is more varying,the length or weight?

If the variance of the distribution is $45.8$,then find the variance of the distribution given below:

$x_i$	$4$	$8$	$11$	$17$	$20$	$24$	$32$
$f_i$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

$y_i$	$10$	$18$	$24$	$36$	$42$	$50$	$66$
$f_i$	$3$	$5$	$9$	$5$	$4$	$3$	$1$

If the mean of $100$ observations is $50$ and their standard deviation is $5$,then the sum of squares of all observations is

The variance of the first $20$ natural numbers is

The average marks of $10$ students in a class was $60$ with a standard deviation of $4$,while the average marks of another $10$ students was $40$ with a standard deviation of $6$. If all the $20$ students are taken together,their combined standard deviation will be: