Question

The variance of the observations $2,3,5,7,11,13,17,22$ is

• A. 43.75
• B. 48.25
• C. 80
• D. 350

Answer 1

Answer: (A)

According to the given information,

$x_i$	$x_i-\bar{x}$	${\left(x_i-\bar{x}\right)}^2$
2	-8	64
3	-7	49
5	-5	25
7	-3	9
11	1	1
13	3	9
17	7	49
22	12	144
$\sum x_i=80$		$\Sigma {\left(x_i-\bar{x}\right)}^2=350$

$\bar{x}=\frac{\Sigma x_i}{8}=\frac{80}{8}=10$
$\because \Sigma {\left(x_i-\bar{x}\right)}^2=350$
$\therefore$ Variance of the given observations $=\frac{\Sigma {\left(x_i-\bar{x}\right)}^2}{8}$
$=\frac{350}{8}=43.75$