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

Question

Philoid · Accepted Answer

Let the assumed mean (A) = 275

Class interval	Mid value (x_i)	d_i = x_i - 275	u_i =	Frequency (f_i)	f_iu_i
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	∑f_iu_i = -35

We have, A = 275

h = 50

Mean = A + h *

= 275 + 50 *

= 275 – 8.75

= 266.25

Expenditure (in rupees) (in rupees)	Frequency (f)	Expenditure (in rupees) (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