Question

The variance of the following frequency distribution is

Class Interval	0 - 6	6 - 12	12 - 18	18 - 24	24 - 30
Frequency	10	8	6	4	2

• A. 56
• B. 30
• C. 11
• D. 20

Answer 1

Answer: (A)

Cl	$f_i$	$x_i$	$f_i{x}_i$	$x_i^2$	$f_i{x}_i^2$
0 - 6	10	3	30	9	90
6 -12	8	9	72	81	648
12 - 18	6	15	90	225	1350
18 - 24	4	21	84	441	1764
24 - 30	2	27	54	729	1458
Total	$\sum f_i=30$		$\sum f_{i}xi=330$		$\sum f_i{x}_i^2=5310$

$\therefore$ Variance $=\frac{1}{N}\sum f_i{x}_i^2-{\left(\frac{\sum f_i{x}_i}{N}\right)}^2$
$=\frac{1}{30}\times 5310-{\left(\frac{330}{30}\right)}^2$
$=177-121=56$