Question

The table below shows the daily expenditure of food of 30 households in a locality:

Daily expenditure (in Rs)	Number of households
100-150	6
150-200	7
200-250	12
250-300	3
300-350	2

Find the mean and median daily expenditare on food.

Answer 1

We have the following:

Daily income	Mid value	Frequency$\left(f_i\right)$	Cumulative frequency	$f_i\times x_i$
100-150	125	6	6	750
150-200	175	7	13	1225
200-250	225	12	25	2700
250-300	275	3	28	825
300-350	325	2	30	650
		∑$f_i=30$		∑$\left(f_i\times x_i\right)=$6150

Mean, $\overline{x}$=$\frac{\sum \left(f_i\times x_i\right)}{\sum f_i}$
=$\frac{6150}{30}$
=205

$$\begin{gathered} \mathrm{Now},N=30 \\ \Rightarrow \frac{N}{2}=15 \end{gathered}$$

The cumulative frequency just greater than 15 is 25 and the corresponding class is 200-250.
Thus, the median class is 200-250.
$\mathrm{Now},l=200,h=50,f=12,c=cf$of preceding class = 13 and $\frac{N}{2}=15$
Median, $M_e=l+\left\{h\times \frac{\left(\frac{N}{2}-c\right)}{f}\right\}$
$$\begin{gathered} =200+\left\{50\times \frac{\left(15-13\right)}{12}\right\} \\ =\left(200+50\times \frac{2}{12}\right) \end{gathered}$$
=200 + 8.33
=208.33