Let $x_1, x_2, \dots, x_n$ be $n$ observations such that $\sum x_i^2 = 300$ and $\sum x_i = 60$. Which of the following is a possible value for $n$?

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

In a distribution of $10$ observations,the sum of the observations is $60$ and the sum of their squares is $1000$. Then,the variance is:

The mean of a distribution is $4$. If its coefficient of variation is $58\%$,what is the standard deviation of the distribution?

$5$ students of a class have an average height $150 \, cm$ and variance $18 \, cm^2$. $A$ new student,whose height is $156 \, cm$,joined them. The variance (in $cm^2$) of the height of these $6$ students is

The standard deviation of the following distribution is:

$C$.$I$.	$0$ - $6$	$6$ - $12$	$12$ - $18$
f_i	$2$	$4$	$6$