Question

Find the mean of each of the following frequency distributions:

Class interval:	0 - 8	8 - 16	16 - 24	24 - 32	32 - 40
Frequency:	6	7	10	8	9

Answer 1

Let the assumed mean (A) = 20

class interval	Mid - value (xi)	di = xi - 20	ui = \(\frac{xi-20}{8}\)	Frequencey (fi)	fiui
0 - 8	4	-16	-2	6	-12
8 - 16	12	-8	-1	7	-17
16 - 24	20	0	0	10	0
24 - 32	28	8	1	8	8
32 - 40	36	16	2	9	18
				N = 40	\(\sum\)fiui = 7

We have,

 A = 20

h = 8

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

= 20 + 8 x \(\frac{7}{40}\)

\(=20 + 1.4 = 21.4\)