The variance of $20$ observations is $5$. If each observation is multiplied by $2$,find the new variance of the resulting observations.

The standard deviation of the following distribution is:

Class interval	$0-10$	$10-20$	$20-30$	$30-40$
Frequency	$1$	$3$	$4$	$2$

In a distribution of $10$ observations,the sum of the observations is $60$ and the sum of their squares is $1000$. Then,the variance is:

Find the standard deviation of the first $n$ natural numbers.

If the mean and variance of the data $65, 68, 58, 44, 48, 45, 60, \alpha, \beta, 60$ where $\alpha > \beta$ are $56$ and $66.2$ respectively,then $\alpha^2 + \beta^2$ is equal to

For a statistical data $x_1, x_2, \ldots, x_{10}$ of $10$ values,a student obtained the mean as $5.5$ and $\sum_{i=1}^{10} x_i^2 = 371$. He later found that he had noted two values in the data incorrectly as $4$ and $5$,instead of the correct values $6$ and $8$,respectively. The variance of the corrected data is