For a frequency distribution,the standard deviation is computed by:

The following table shows the marks obtained by two students,Ravi and Hashina,in $10$ tests (out of $100$ marks each).

Student	Marks
Ravi	$25, 50, 45, 30, 70, 42, 36, 48, 35, 60$
Hashina	$10, 70, 50, 20, 95, 55, 42, 60, 48, 80$

Who is more intelligent and who is more consistent?

What is the standard deviation of the following series?

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

The variance of the first $10$ natural numbers which are multiples of $3$ is

Let $x_1, x_2, x_3, \dots, x_n$ be $n$ observations,$\bar{x}$ be their arithmetic mean,and $\sigma^2$ be their variance.
Statement $-1$: The variance of observations $2x_1, 2x_2, 2x_3, \dots, 2x_n$ is $4\sigma^2$.
Statement $-2$: The arithmetic mean of $2x_1, 2x_2, 2x_3, \dots, 2x_n$ is $4\bar{x}$.

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 $\frac{n(4n^2 - 1)}{3}$.