Question

The variance of observations $112,116,120,125,132$ is

• A. $58.8$
• B. $48.8$
• C. $61.8$
• D. None of these

Answer 1

The correct option is B $48.8$

Given observations $112,116,120,125,132$.
$\overline{x}=\frac{\Sigma x_1}{n}=\frac{605}{5}=121$

$x_i$	$x_i-\overline{x}$	$(x_i-\overline{x}{)}^2$
112	-9	81
116	-5	25
120	-1	1
125	4	16
132	11	121

$\Sigma {(x_i-\overline{x})}^2=81+25+1+16+121=244$
$\therefore {\sigma }^2=\frac{\Sigma {(x_i-\overline{x})}^2}{n}$
$\sigma =\frac{244}{5}=48.8$