Question

Find the variance for the following data: $6,4,8,5,2,17$

Answer 1

$\Rightarrow$ Arranging given numbers in ascending order $2,4,5,6,8,17$

$\Rightarrow$ Mean $\left(\overline{x}\right)=\frac{2+4+5+6+8+17}{6}=\frac{42}{6}=7$

$x$	$x-\overline{x}$	$(x-\overline{x}{)}^2$
$2$	$-5$	$25$
$4$	$-3$	$9$
$5$	$-2$	$4$
$6$	$-1$	$1$
$8$	$1$	$1$
$17$	$10$	$100$
		$\sum (x-\overline{x}{)}^2=146$

$\Rightarrow$ Variance $\left({\sigma }^2\right)=\frac{\sum (x-\overline{x}{)}^2}{6}$

$=\frac{140}{6}$

$=23.33$