The variance of the first $20$ natural numbers is

The mean and variance of $n$ observations $x_1, x_2, x_3, \ldots, x_n$ are $5$ and $0$ respectively. If $\sum_{i=1}^n x_i^2 = 400$,then the value of $n$ is equal to

The mean square deviation of a set of observations $x_1, x_2, \dots, x_n$ about a point $c$ is defined as $\frac{1}{n} \sum_{i=1}^n (x_i - c)^2$. If the mean square deviations about $-2$ and $2$ are $18$ and $10$ respectively,find the standard deviation of this set of observations.

If the median of the data $6, 7, x-2, x, 18$ and $21$ written in ascending order is $16$,then the variance of that data is

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

If $X$ is a random variable such that $\sigma(X) = 2.6$, then $\sigma(1 - 4X)$ is equal to: