For a given distribution of marks,the mean is $35.16$ and its standard deviation is $19.76$. The coefficient of variation is:

The mean and standard deviation of marks obtained by $50$ students of a class in three subjects,Mathematics,Physics and Chemistry are given below:

Subject	Mathematics,Physics,Chemistry
Mean	$42, 32, 40.9$
Standard deviation	$12, 15, 20$

Which of the three subjects shows the highest variability in marks and which shows the lowest?

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 $4\bar{x}$.

If the mean and standard deviation of $n$ observations $x_1, x_2, \dots, x_n$ are $\bar{x}$ and $\sigma$ respectively,then what is the sum of the squares of the observations?

If each of the observations $x_{1}, x_{2}, \ldots, x_{n}$ is increased by $a$,where $a$ is a positive or negative number,show that the variance remains unchanged.

The $S.D.$ of $15$ items is $6$. If each item is decreased or increased by $1$,then the standard deviation will be: