Question

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

Daily expenditure (in Rs)	Number of households
100-150	6
150-200	7
20-250	12
250-300	3
300-350	2

Find the mean and median of daily expenditure on food.

Answer 1

Let the assumed mean A be 225; h = 50.
$\mathrm{Mean},\overline{\mathrm{x}}=\mathrm{A}+\left\{\mathrm{h}\times \frac{\sum \left({\mathrm{f}}_{\mathrm{i}}\times {\mathrm{u}}_{\mathrm{i}}\right)}{\sum {\mathrm{f}}_{\mathrm{i}}}\right\}$
$$\begin{gathered} =225+\left\{50\times \frac{-12}{30}\right\} \\ =225-20 \\ =205 \end{gathered}$$
Now,
$\frac{N}{2}=\frac{30}{2}=15$
Cumulative frequency just after 15 is 25.
Corresponding class interval is 200 - 250.
Median class is 200 - 250.
Cumulative frequency just before this class = 13
So, l = 200, f = 12 , $\frac{N}{2}=15$, h = 50 and cf = 13
$\mathrm{Median},M_e=l+\left\{h\times \frac{\left({\displaystyle \frac{N}{2}}-cf\right)}{f}\right\}$
$$\begin{gathered} =200+50\left(\frac{15-13}{12}\right) \\ =200+\frac{50\times 2}{12} \\ =200+\frac{25}{3} \\ =200+8.33 \\ =208.33 \end{gathered}$$
Hence, mean = 205 and median = 208.33