Question

The table below shows the daily expenditure on food of 25 households in a locality.

Daily expenditure (in Rs):	100 - 150	150 - 200	200 - 250	250 - 300	300 - 350
Number of households:	4	5	12	2	2

Find the mean daily expenditure on food by a suitable method.

Answer 1

We may calculate class marks (x_i) for each interval by using the relation

x_i \(=\frac{Upper\,class\,limit+lower\,class\,limits}{2}\)

Class size = 50

Now taking 225 as assumed mean we can calculate as follows:

Daily expenditure (in Rs)	fi	di = xi - A = xi - 225	ui = \(\frac{xi-225}{h}\)	xi	fiui
100 - 150	4	-100	-2	125	-8
150 - 200	5	-50	-1	175	-5
200 - 250	12	0	0	225	0
250 - 300	2	50	1	275	2
300 - 350	2	100	2	325	4
	N = 25				\(\sum\)fiui = -7

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

\(=225+\frac{-7}{25}\times50\)

\(=225-14=211\)

So mean expenditure on food is 211