If the standard deviation of $0, 1, 2, 3, \dots, 9$ is $K$,then the standard deviation of $10, 11, 12, 13, \dots, 19$ is

In a discrete data,$\frac{1}{4}$ of the observations are equal to $a$,another $\frac{1}{4}$ of the observations are equal to $-a$. Out of the remaining,half of them are equal to $b$ and the rest are equal to $-b$. If the variance of all the observations is $ab$,then:

Find the variance of the following frequency distribution.

$Class$	$0-2$	$2-4$	$4-6$	$6-8$	$8-10$	$10-12$
$f_i$	$2$	$7$	$12$	$19$	$9$	$1$

The variance and mean of $15$ observations are respectively $6$ and $10$. If each observation is increased by $8$,then the new variance and new mean of the resulting observations are respectively:

If the data $x_1, x_2, ..., x_{10}$ is such that the mean of the first four of these is $11$,the mean of the remaining six is $16$,and the sum of squares of all of these is $2,000$; then the standard deviation of this data is

The means of two groups of size $200$ and $300$ are $25$ and $10$ respectively. Their standard deviations are $3$ and $4$ respectively. What is the variance of the combined sample of size $500$?