The mean and variance of eight observations are $9$ and $9.25,$ respectively. If six of the observations are $6, 7, 10, 12, 12,$ and $13,$ find the remaining two observations.

The mean and standard deviation of the marks of $10$ students were found to be $50$ and $12$ respectively. Later,it was observed that two marks $20$ and $25$ were wrongly read as $45$ and $50$ respectively. Then the correct variance is $............$.

The mean and variance of $7$ observations are $8$ and $16$ respectively. If one observation $14$ is omitted and $a$ and $b$ are respectively the mean and variance of the remaining $6$ observations,then $a+3b-5$ is equal to $..........$.

In a town,the probability that a sick person may need to be admitted to an $ICU$ is $10 \%$. If the probability that a person getting admitted to an $ICU$ goes above $5 \%$,then the threat level is raised. The minimum percentage of the population of the town that should fall sick in order to raise the threat level is

Let $a, b, c \in N$ and $a < b < c$. Let the mean,the mean deviation about the mean,and the variance of the $5$ observations $9, 25, a, b, c$ be $18, 4$,and $\frac{136}{5}$,respectively. Then $2a + b - c$ is equal to:

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 $............$.

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