The variance of $10$ observations is $16$. If each observation is doubled,then the standard deviation of the new data will be -

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?

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 $9$ items $x_1, x_2, ..., x_9$ is:

Find the mean and variance for the following data:

$x_i$	$6$	$10$	$14$	$18$	$24$	$28$	$30$
$f_i$	$2$	$4$	$7$	$12$	$8$	$4$	$3$

Statement $1$: The variance of the first $n$ odd natural numbers is $\frac{n^2 - 1}{3}$.
Statement $2$: The sum of the first $n$ odd natural numbers is $n^2$ and the sum of the squares of the first $n$ odd natural numbers is $\frac{n(4n^2 - 1)}{3}$.

Let $X = \{x \in \mathbb{N} : 1 \le x \le 19\}$ and for some $a, b \in \mathbb{R}$, $Y = \{ax + b : x \in X\}$. If the mean and variance of the elements of $Y$ are $30$ and $750$, respectively, then the sum of all possible values of $b$ is