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.

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

The mean and variance of a data of $10$ observations are $10$ and $2$,respectively. If an observation $\alpha$ in this data is replaced by $\beta$,then the mean and variance become $10.1$ and $1.99$,respectively. Then $\alpha + \beta$ equals.

Mean and standard deviation of $100$ observations were found to be $40$ and $10$,respectively. If at the time of calculation,two observations were wrongly taken as $30$ and $70$ in place of $3$ and $27$ respectively,find the correct standard deviation.

The mean and the standard deviation of $10$ observations are $20$ and $2$ respectively. Each of these $10$ observations is multiplied by $p$ and then reduced by $q$,where $p \neq 0$ and $q \neq 0$. If the new mean and new standard deviation (s.d.) become half of the original values,then $q$ is equal to

If the mean of the following frequency distribution is $2.6$,find the value of $f$.

$x_i$	$1$	$2$	$3$	$4$	$5$
$f_i$	$5$	$4$	$f$	$2$	$3$