Following table shows distribution of monthly expenditure (in Rs.) done by households in a certain village on electricity : Find median expenditure done by a household on electricity per month.
| Monthly expenditure | 150 - 225 | 225 - 300 | 300 - 375 | 375 - 450 | 450 - 525 | 525 - 600 | 600 and above |
|---|---|---|---|---|---|---|---|
| No. of households | 65 | 171 | 196 | 75 | 53 | 26 | 14 |
Solution:
Classes
(Monthly exp.)Frequency ($f_i$)
(No. of households)Cumulative frequency
less than type150 - 225 65 65 225 - 300 171 236 → $c.f.$ 300 - 375 196 → $f$ 432 375 - 450 75 507 450 - 525 53 560 525 - 600 26 586 600 and above 14 600 Total 600 → N Here total frequency = $\Sigma f_i = N = 600$
$\frac{N}{2} = \frac{600}{2} = 300$
Cumulative frequency (less than type) which is just greater than 300 is 432. Therefore corresponding class 300 - 375 is median class.
$L = 300$, $N = 600$, $c.f. = 236$, $f = 196$, $h = 75$
$$ \text{Median} = L + \left( \frac{N}{2} - c.f. \right) \frac{h}{f} $$ $$ = 300 + \left( \frac{600}{2} - 236 \right) \frac{75}{196} $$ $$ = 300 + (300 - 236) \frac{75}{196} $$ $$ = 300 + (64) \frac{75}{196} $$ $$ = 300 + 16 \left( \frac{75}{49} \right) $$ $$ = 300 + \frac{1200}{49} $$ $$ = 300 + 24.49 $$ $$ = 324.49 $$Median of monthly expenditure is Rs. 324.49.