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 of $6$ distinct observations is $6.5$ and their variance is $10.25$. If $4$ out of $6$ observations are $2, 4, 5$ and $7$,then the remaining two observations are:

If the mean and variance of the frequency distribution are $9$ and $15.08$ respectively,then the value of $\alpha^2+\beta^2-\alpha \beta$ is $............$.

$x_i$	$2$	$4$	$6$	$8$	$10$	$12$	$14$	$16$
$f_i$	$4$	$4$	$\alpha$	$15$	$8$	$\beta$	$4$	$5$

$A$ problem in statistics is given to three students $P, Q$ and $R$. Their chances of solving the problem are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. If all of them try independently,then the probability that the problem is solved is:

If $x_1, x_2, \ldots, x_n$ are $n$ observations and $\bar{x}$ is their mean. If $\sum_{i=1}^{n}(x_i - \bar{x})^2$ is almost zero,then which of the following statements is true?

Consider the following frequency distribution:

Class:	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Freq:	$\alpha$	$110$	$54$	$30$	$\beta$

If the sum of all frequencies is $584$ and the median is $45$,then $|\alpha-\beta|$ is equal to $.....$