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

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

The following values are calculated in respect of heights and weights of the students of a section of Class $\mathrm{XI}:$

Can we say that the weights show greater variation than the heights?

Find the mean and variance for the first $n$ natural numbers

Let the mean and variance of $12$ observations be $\frac{9}{2}$ and $4$ respectively. Later on, it was observed that two observations were considered as $9$ and $10$ instead of $7$ and $14$ respectively. If the correct variance is $\frac{m}{n}$, where $m$ and $n$ are co-prime, then $m + n$ is equal to

The mean and standard deviation of $40$ observations are $30$ and $5$ respectively. It was noticed that two of these observations $12$ and $10$ were wrongly recorded. If $\sigma$ is the standard deviation of the data after omitting the two wrong observations from the data, then $38 \sigma^{2}$ is equal to$.........$

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.