If the variance of the frequency distribution is $160$,then the value of $c \in N$ is

$X$	$c$	$2c$	$3c$	$4c$	$5c$	$6c$
$f$	$2$	$1$	$1$	$1$	$1$	$1$

The mean and standard deviation of $100$ items are $50$ and $4$,respectively. Find the sum of all the items and the sum of the squares of the items.

The mean and standard deviation of a distribution of weights of a group of $20$ boys are $40 \ kg$ and $5 \ kg$ respectively. If two boys of weights $43 \ kg$ and $37 \ kg$ are excluded from this group,then the variance of the distribution of weights of the remaining group of boys is

The variance of the observations $112, 116, 120, 125, 132$ is $......$

If both the mean and the standard deviation of $50$ observations $x_1, x_2, \dots, x_{50}$ are equal to $16$,then the mean of $(x_1 - 4)^2, (x_2 - 4)^2, \dots, (x_{50} - 4)^2$ is

In a data set with $15$ observations $x_1, x_2, x_3, \ldots, x_{15}$,we are given $\sum_{i=1}^{15} x_i^2 = 3600$ and $\sum_{i=1}^{15} x_i = 175$. If the value of one observation $20$ was found to be incorrect and was replaced by its correct value $40$,then the corrected variance of the data is: