The mean and standard deviation of $15$ observations were found to be $12$ and $3$ respectively. On rechecking,it was found that an observation was read as $10$ in place of $12$. If $\mu$ and $\sigma^2$ denote the mean and variance of the correct observations respectively,then $15(\mu+\mu^2+\sigma^2)$ is equal to $...................$

Let the mean and variance of $8$ numbers $-10, -7, -1, x, y, 9, 2, 16$ be $\frac{7}{2}$ and $\frac{293}{4}$ respectively. Then the mean of $4$ numbers $x, y, x + y + 1, |x - y|$ is:

Let $x_1, x_2, \ldots, x_{11}$ be the observations satisfying $\sum_{i=1}^{11}(x_i-4)=22$ and $\sum_{i=1}^{11}(x_i-4)^2=154$. If the mean and variance of the observations are $\alpha$ and $\beta$,then the quadratic equation having the roots $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$ is

Let the mean of the data be $5$.

$X$	$1$	$3$	$5$	$7$	$9$
$f$	$4$	$24$	$28$	$\alpha$	$8$

If $m$ and $\sigma^2$ are respectively the mean deviation about the mean and the variance of the data,then $\frac{3 \alpha}{m+\sigma^2}$ is equal to $..........$.

For a group of $100$ students,the mean $\bar{x}_1$ and the standard deviation $\sigma_1$ of their marks were found to be $40$ and $15$ respectively. Later,it was observed that the scores $40$ and $50$ were misread as $30$ and $60$ respectively. If the mean and the standard deviation with the corrected observations of the scores are $\bar{x}_2$ and $\sigma_2$ respectively,then:

$A$ pie chart is to be drawn for representing the following data. The value of the central angle for food and clothing would be...$^o$

Items of expenditure	Number of families
$Education$	$150$
$Food and clothing$	$400$
$House rent$	$40$
$Electricity$	$250$
$Miscellaneous$	$160$