The variance of the first $10$ multiples of $3$ is:

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 frequency distribution:
$\begin{array}{|l|l|l|l|l|l|l|} \hline X & A & 2 A & 3 A & 4 A & 5 A & 6 A \\ \hline f & 2 & 1 & 1 & 1 & 1 & 1 \\ \hline \end{array}$
where $A$ is a positive integer,has a variance of $160$. Determine the value of $A$.

Let $x_1, x_2, \dots, x_n$ be the values taken by a variable $X$ and $y_1, y_2, \dots, y_n$ be the values taken by a variable $Y$ such that $y_i = ax_i + b$,where $i = 1, 2, \dots, n$. Then...

$5$ 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

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 these observations is $2$,then $|a|$ equals: