Question

The variance of the following continuous frequency distribution is

Class Interval	0-10	10-20	20-30	30-40
Frequency	2	3	4	1

• A. 201
• B. 62
• C. 19
• D. 84

Answer 1

Answer: (D)

Given

Class Interval	Frequency $(f_i)$	$x_i$	$x_i{f}_i$	${\left(\bar{x}-x_i\right)}^2$	$f_i{\left(\bar{x}-x_i\right)}^2$
0-10	2	5	10	196	392
10-20	3	15	45	16	48
20-30	4	25	100	36	144
30-40	1	35	35	256	256
	$N=\Sigma f_i=10$		$\Sigma x_i{f}_i=190$		$\Sigma f_i{\left(\bar{x}-x_i\right)}^2=840$

$\because \bar{x}=\frac{\sum x_i{f}_i}{N}=\frac{190}{10}=19$
$\therefore$ Variance $(\sigma {)}^2=\frac{1}{N}\Sigma f_i{\left(\bar{x}-x_i\right)}^2$
$=\frac{1}{10}(840)=84$