The mean and variance of $20$ observations are found to be $10$ and $4,$ respectively. On rechecking,it was found that an observation $9$ was incorrect and the correct observation was $11$. Then the correct variance is

The mean and variance of $7$ observations are $8$ and $16$ respectively. If two observations are $6$ and $8$,then the variance of the remaining $5$ observations is:

The mean of $100$ observations is $45$. It was later found that two observations $19$ and $31$ were incorrectly recorded as $91$ and $13$. The correct mean is...

If $x_1, x_2, \ldots, x_n$ are $n$ observations such that $\sum_{i=1}^n x_i^2 = 400$ and $\sum_{i=1}^n x_i = 80$,then the least value of $n$ is

The mean and standard deviation of $50$ observations are $15$ and $2$ respectively. It was found that one incorrect observation was taken such that the sum of the correct and incorrect observations is $70$. If the correct mean is $16$,then the correct variance is equal to

The mean of the following frequency distribution is $50$ and $\Sigma f = 120$. Find the missing frequencies $f_1$ and $f_2$.

Class	$0-20$	$20-40$	$40-60$	$60-80$	$80-100$
$f$	$17$	$f_1$	$32$	$f_2$	$19$