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

To find the class mark ($x_i$) for each interval, the following relation is used.

Class mark $(x_i)$ = $\frac {\text{Upper \,limit + Lower \,limit}}{2}$

class size (h) of the data = 50

Taking 225 as assured mean (a), $d_i$, $u_i$, and $f_iu_i$ can be calculated as follows.

**Daily expenditure (in Rs) **	** ($\bf{f_i}$) **	** $\bf{x_i}$ **	$\bf{d_i = x_i -225}$	$\bf{u_i = \frac{d_i}{50}}$	$\bf{f_iu_i}$
**100 - 150 **	4	125	-100	-2	-8
150 - 200	5	175	-50	-1	-5
200 - 250	12	225	0	0	0
250 - 300	2	275	50	1	2
300 - 350	2	325	100	2	4
**Total **	** 25**				-7

From the table, it can be observed that

$\sum f_i = 25$
$\sum f_iu_i = -7$

Mean, $\overset{-}{x} = a + (\frac{\sum f_iu_i}{\sum f_i}) \times h$

x = $225 \+ (\frac{-7 }{25})\times 50$

x = 225 - 14

x = 211

Therefore, mean daily expenditure on food is Rs 211.