Question

The following table gives the distribution of total household expenditure (in rupees) of manual workers in a city.

Expenditure (in rupees)	Frequency (f)	Expenditure (in rupess) (x)	Frequency  (f)
100+150	24	300-350	30
150-200	40	350-400	22
200-250	33	400-450	16
250-300	28	450-500	7

Find the average expenditure (in rupees) per household.

Answer 1

Let the assumed mean (A) = 275

Class interval	Mid value (xi)	di = xi - 275	ui = \(\frac{xi-275}{50}\)	Frequency (fi)	fiui
100 - 150	125	-150	-3	24	-72
150 - 200	175	-100	-2	40	-80
200 - 250	225	-50	-1	33	-33
250 - 300	275	0	0	28	0
300 - 350	325	50	1	30	30
350 - 400	375	100	2	22	44
400 - 450	425	150	3	16	48
450 - 500	475	200	4	7	28
				N = 200	\(\sum\)fiui = -35

We have, 

A = 275

h = 50

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

\(=275+50\times\frac{-35}{200}\)

= 275 – 8.75

= 266.25