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.