Question

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

Daily Expenditure (Rs.)	100 - 150	150 - 200	200 - 250	250 - 300	300 - 350
No. of Households	4	5	12	2	2

Answer 1

By Step deviation method :

Daily expenditure	No. of households $$ f_{1} $$	Mid- point $$ x_{1} $$	$$ u_{1} = $$ $$ \dfrac{x_{1} - 225}{50} $$	$$ f_{1} \times u_{1} $$
100 - 150	4	125	-3	-8
150 - 200	5	175	-1	-5
200 - 250	12	225	0	0
250 - 300	2	275	1	2
300 - 350	2	325	2	4
	$$ n = 30 $$			-7

Here , let $$ a = 225 $$
$$ h = 50, n = 25, \sum f_{1}u_{1} = -7 $$
$$ \bar{X} = a + h \times \dfrac{1}{n} \times \sum f_{1}u_{1} $$
$$ = 225 + 50 \times \dfrac{1}{25} \times (-7) $$
$$ = 225 - 14 $$
$$ = 211 $$
$$ \therefore $$ Mean Daily expenditure for food = Rs 211.