Question

Find the mean of each of the following frequency distributions:

Class interval:	0 - 10	10 - 12	20 - 30	30 - 40	40 - 50
Frequency:	9	12	15	10	14

Answer 1

Let the assumed mean (A) = 25

class interval	Mid value (xi)	di = xi - 25	ui = \(\frac{xi-25}{10}\)	Frequency (fi)	fiui
0 - 10	5	-20	-2	9	-18
10 - 20	15	-10	-1	12	-12
20 - 30	25	0	0	15	0
30 - 40	35	10	1	10	10
40 - 50	45	20	2	14	28
				N = 60	\(\sum\)fiui = 8

We have, 

A = 25

h = 10

Mean = A + h x \(\frac{\sum f_iu_i}{N}\)

\(=25+10\times\frac{8}{60}\)

\(=25+\frac{8}{6}\)

\(=25+\frac{4}{3}=26.333\)