The average marks of boys in a class is $52$ and that of girls is $42$. If the combined average of boys and girls is $50$,find the percentage of boys in the class.

The mean and standard deviation of $20$ observations are found to be $10$ and $2$,respectively. It was later discovered that one observation was mistakenly recorded as $8$ instead of $12$. The correct standard deviation is:

If the mean of the data:

Class	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$
Frequency	$2$	$k$	$28$	$54$	$k + 1$	$5$

is $21$,then $k$ is one of the roots of the equation:

The mean of the numbers $a, b, 8, 5, 10$ is $6$ and the variance is $6.8$. Then which of the following gives possible values of $a$ and $b$?

Let sets $A$ and $B$ have $5$ elements each. Let the mean of the elements in sets $A$ and $B$ be $5$ and $8$ respectively,and the variance of the elements in sets $A$ and $B$ be $12$ and $20$ respectively. $A$ new set $C$ of $10$ elements is formed by subtracting $3$ from each element of $A$ and adding $2$ to each element of $B$. Then the sum of the mean and variance of the elements of $C$ is $.......$.

If the sum of squares of the deviations from the mean of the data $x_i, (i=1, 2, \ldots, n)$ is $n\bar{x}^2$,where $\bar{x}$ is the mean of $x_i$'s,then the sum of squares of $x_i$'s is