If the standard deviation of $x_i$ is $10$,what will be the variance of $(50 + 5x_i)$?

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

Students of two sections $A$ and $B$ of a class show the following results in a test conducted for $100$ marks. Then

	Section $A$	Section $B$
Number of students	$50$	$60$
Average marks in the test	$45$	$45$
Variance of distribution of marks	$64$	$81$

In a series of $2n$ observations,half of them are equal to $a$ and the remaining half are equal to $-a$. If the standard deviation of the observations is $2$,then $|a|$ equals:

The frequency distribution is given below:
$\begin{array}{|l|l|l|l|l|l|l|} \hline X & 2 & 3 & 4 & 5 & 6 & 7 \\ f & 4 & 9 & 16 & 14 & 11 & 6 \\ \hline \end{array}$
Find the standard deviation.

Find the mean and variance for the first $10$ multiples of $3$.