The mean of two samples of size $200$ and $300$ were found to be $25$ and $10$ respectively. Their standard deviations $(S.D.)$ are $3$ and $4$ respectively. Then,the variance of the combined sample of size $500$ is:

The variance of $20$ observations is $5$. If each of the observations is multiplied by $2$,then the variance of the resulting observations is:

If both the mean and the standard deviation of $50$ observations $x_1, x_2, \dots, x_{50}$ are equal to $16$,then the mean of $(x_1 - 4)^2, (x_2 - 4)^2, \dots, (x_{50} - 4)^2$ is

If $\sum_{i=1}^9(x_i-5)=9$ and $\sum_{i=1}^9(x_i-5)^2=45$,then the standard deviation of the nine observations $x_1, x_2, \ldots, x_9$ is

The coefficient of variation for the following data is:

$x_i$	$5$	$7$	$9$	$11$
$f_i$	$3$	$2$	$1$	$2$

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