Question

Find the mean of each of the following frequency distributions:

Class interval:	10 - 30	30 - 50	50 - 70	70 - 90	90 - 110	110 - 130
Frequency:	5	8	12	20	3	2

Answer 1

Let the assumed mean (A) = 60

Class interval	Mid value (xi)	di = xi - 60	ui = \(\frac{xi-60}{20}\)	Frequency (fi)	fiui
10 - 30	20	-40	-2	5	-10
30 - 50	40	-20	-1	8	-8
50 - 70	60	0	0	12	0
70 - 90	80	20	1	20	20
90 - 110	100	40	2	3	6
110 - 130	120	60	3	2	6
				N = 50	\(\sum\)fiui= 14

We have, 

A = 60 

h = 20 

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

= 60 + 20 \(\times\frac{14}{50}\) 

= 60 + 5.6 

= 65.6