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

Problem Statement: The class mark (\(x_i\)) for each interval is calculated using the formula: Class mark (\((x_i)\)) = \(\frac {\text{Upper \,limit + Lower \,limit}}{2}\).

The class size (h) for this data set is 50.

With 225 designated as the assumed mean (a), the values for \(d_i\), \(u_i\), and \(f_i u_i\) are determined as follows.

Daily expenditure (in Rs)	(\(\bf{f_i}\))	\(\bf{x_i}\)	\(\bf{d_i = x_i -17}\)	\(\bf{u_i = \frac{d_i}{50}}\)	\(\bf{f_i u_i}\)
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				-181

The table yields the following summations:

\(\sum f_i = 25\)
\(\sum f_i u_i = -181\)

The mean is computed using the formula: Mean (\(\overset{-}{x}\)) = \(a + (\frac{\sum f_i u_i}{\sum f_i}) \times h\).

Substituting the values: Mean (\(\overset{-}{x}\)) = \(225 + (\frac{-181}{25}) \times 50\).

Mean (\(\overset{-}{x}\)) = 225 - 14.

Mean (\(\overset{-}{x}\)) = 211.

Consequently, the average daily expenditure on food is Rs 211.