The average marks of $10$ students in a class was $60$ with a standard deviation of $4$,while the average marks of another $10$ students was $40$ with a standard deviation of $6$. If all the $20$ students are taken together,their combined standard deviation will be:

All students in a classroom performed poorly in mathematics. The teacher decided to increase the marks of each student by $10$. Which of the following statistical measures will not change even after adding the extra marks?

The mean and variance of six observations are $6$ and $12$ respectively. If each observation is multiplied by $3$,then the new variance of the resulting observations is:

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

$5$ students of a class have an average height $150 \, cm$ and variance $18 \, cm^2$. $A$ new student,whose height is $156 \, cm$,joined them. The variance (in $cm^2$) of the height of these $6$ students is

If for a distribution,$\Sigma(x-5)=3$ and $\Sigma(x-5)^2=43$ and the total number of observations is $18$,then the variance of the distribution is