Question

Find the mean of each of the following frequency distributions:

Class interval:	0 - 8	8 - 16	16 - 24	24 - 32	32 - 40
Frequency:	5	9	10	8	8

Answer 1

Let the assumed mean (A) = 20

class interval	Mid value (xi)	di = xi - 20	ui = \(\frac{xi-20}{8}\)	Frequency (fi)	fiui
0 - 8	4	-16	-2	5	-10
8 - 16	12	-8	-1	9	-9
16 - 24	20	0	0	10	0
24 - 32	28	8	1	8	8
32 - 40	36	16	2	8	16
				N = 40	\(\sum\)fiui = 5

We have, 

A = 20

h = 8

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

\(=20 + 8 \times\frac{5}{40}\)

\(=20+1.4 = 21.4\)