If the standard deviation of the first $n$ natural numbers is $2$,then the value of $n$ is

Let $a, b, c, d$ and $e$ be the observations with mean $m$ and standard deviation $S$. The standard deviation of the observations $a+k, b+k, c+k, d+k$ and $e+k$ is

Find the mean and variance for the first $10$ multiples of $3$.

The variance of the following frequency distribution is:

Classes	$0-10$	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$
Frequency	$11$	$29$	$18$	$4$	$5$	$3$

If each of the observations $x_{1}, x_{2}, \ldots, x_{n}$ is increased by $a$,where $a$ is a positive or negative number,show that the variance remains unchanged.

The mean of four observations is $3$. If the sum of the squares of these observations is $48$,then their standard deviation is