The following table shows the information about marks obtained in Physics,Chemistry,Mathematics,and Biology by $100$ students in a class. Which subject shows the highest variability in marks?

	Physics	Chemistry	Mathematics	Biology
Mean	$20$	$25$	$23$	$27$
$S$.$D$.	$3$	$2$	$4$	$5$

For a data consisting of $15$ observations $x_i$,$i=1, 2, 3, \ldots, 15$,the following results are obtained: $\sum_{i=1}^{15} x_i = 170$ and $\sum_{i=1}^{15} x_i^2 = 2830$. If one of the observations,namely $20$,was found to be wrong and was replaced by its correct value $30$,then the corrected variance is:

What is the standard deviation of the following series?

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

Find the mean and variance for the data $6, 7, 10, 12, 13, 4, 8, 12$.

Calculate the variance of the following continuous frequency distribution:

Class Interval	$0$–$4$	$4$–$8$	$8$–$12$	$12$–$16$
Frequency $(f_i)$	$1$	$2$	$2$	$1$

If $\sum_{i=1}^{5}(x_i-10)=5$ and $\sum_{i=1}^{5}(x_i-10)^2=5$,then the standard deviation of the observations $2x_1 + 7, 2x_2 + 7, 2x_3 + 7, 2x_4 + 7,$ and $2x_5 + 7$ is equal to-