Question

Find the mean and variance for the following frequency distribution.

Classes	0-10	10-20	20-30	30-40	40-50
Frequencies	5	8	15	16	6

Answer 1

Class	Frequency \(f_i\)	\(mid-point\,x_i\)	\(y_i=\frac{x_i-25}{10}\)	\(y_i^2\)	\(f_iy_i\)	\(f_iy_1^2\)
0-10	5	5	-2	4	-10	20
10-20	8	15	-1	1	-8	8
20-30	15	25	0	0	0	0
30-40	16	35	1	1	16	16
40-50	6	45	2	12	12	24
	50				10	68

Mean,  \(\bar{x}=A\frac{\sum_{i=1}^5f_ix_i}{n}×h=25+\frac{10}{50}×10=25+2=27\) 

Variance (σ²) = \(\frac{h^2}{N^2}[N\sum_{i=1}^5f_iy_i^2-(\sum_{i=1}^5f_iy_i)^2]\)

\(=\frac{(10)^2}{(50)^2}[50×68-(10)^2]\)

\(\frac{1}{25}[3400-100]=\frac{3300}{25}\)

\(=132\)