For $20$ observations of variable $x$,if $\sum(x_{i}-2)=20$ and $\sum(x_{i}-2)^2=100$,then the standard deviation of variable $x$ is

The variance of the ungrouped data $2, 12, 3, 11, 5, 10, 6, 7$ is

If each observation of a distribution with variance $\sigma^2$ is multiplied by $\lambda$,find the standard deviation of the new observations.

If the mean of the discrete distribution $8, 9, 6, 5, x, 4, 6, 5$ is $6$,then its standard deviation (nearest to two decimal places) is

Given that $\bar{x}$ is the mean and $\sigma^{2}$ is the variance of $n$ observations $x_{1}, x_{2}, \ldots, x_{n}$,prove that the mean and variance of the observations $a x_{1}, a x_{2}, \ldots, a x_{n}$ are $a \bar{x}$ and $a^{2} \sigma^{2}$ respectively,where $a \neq 0$.

If the sum of $10$ observations and the sum of their squares are $12$ and $18$ respectively,then the standard deviation of the observations is: