The table below shows expenditure on food of 25 households in a locality. Find the mean daily expenditure on food by a suitable method.

Question :

Daily expenditure (in Rupees)	100 – 150	150 – 200	200 – 250	250 – 300	300 – 350
Number of households	4	5	12	2	2

Solution :

Let the assumed mean, A = 225, class size, h = 50

So, \(u_i\) = \(x_i – A\over h\) = \(x_i – 225\over 50\)

Daily expenditure (in Rupees)	Mid – Values (\(x_i\))	Frequency (\(x_i\))	\(u_i\) = \(x_i – 225\over 50\)	\(f_iu_i\)
100 – 150	125	4	-2	-8
150 – 200	175	5	-1	-5
200 – 250	175	12	0	0
250 – 300	225	2	1	2
300 – 350	325	2	2	4
Total		25		-7

So, Mean = A + h\(\sum f_iu_i\over \sum f_i\) = 225 + 50 \(\times\) \(-7\over 25\) = 225 – 14 = 211

Hence, the mean daily expenditure on food is 211 rupees.