The mean and variance of $5$ observations are $4$ and $5.2$ respectively. If three of these observations are $1, 2,$ and $6,$ find the other two observations.

Let the mean and variance of the frequency distribution be $6$ and $6.8$ respectively.

$x$	$2$	$6$	$8$	$9$
$f$	$4$	$4$	$\alpha$	$\beta$

If $x_{3}$ is changed from $8$ to $7$,then the mean for the new data will be:

Let $a$ and $b$ be two real numbers. If the arithmetic mean and the variance of $a, b, 8, 5$ and $10$ are respectively $6$ and $6.8$,then an ordered pair $(a, b) =$

Let $X = \{11, 12, 13, \ldots, 40, 41\}$ and $Y = \{61, 62, 63, \ldots, 90, 91\}$ be two sets of observations. If $\bar{x}$ and $\bar{y}$ are their respective means and $\sigma^2$ is the variance of all the observations in $X \cup Y$,then $|\bar{x} + \bar{y} - \sigma^2|$ is equal to $.................$.

If the mean and variance of eight numbers $3, 7, 9, 12, 13, 20, x$,and $y$ are $10$ and $25$ respectively,then $x \cdot y$ is equal to

The average marks of boys in a class is $40$ and that of girls is $45$. The average marks of both boys and girls combined is $42$. Then the percentage of boys in the class is (in $\%$)