Following is the distribution of the size of certain farms from a taluka (tehasil) :
| Size of farm (in acres) |
5 - 15 | 15 - 25 | 25 - 35 | 35 - 45 | 45 - 55 | 55 - 65 | 65 - 75 |
|---|---|---|---|---|---|---|---|
| No. of farms | 7 | 12 | 17 | 25 | 31 | 5 | 3 |
Find median size of a farm.
Solution:
Size of farm
(in acres)Frequency ($f_i$)
(No. of farms)Cumulative frequency
less than type5 - 15 7 7 15 - 25 12 19 25 - 35 17 36 $\rightarrow c.f.$ 35 - 45 25 $\rightarrow f$ 61 45 - 55 31 92 55 - 65 5 97 65 - 75 3 100 Total 100 $\rightarrow$ N Here total frequency = $\Sigma f_i = N = 100$
$\therefore \frac{N}{2} = \frac{100}{2} = 50$
Cumulative frequency (less than type) which is just greater than 50 is 61. Therefore corresponding class 35 - 45 is median class.
$L = 35$, $N = 100$, $c.f. = 36$, $f = 25$, $h = 10$Median $= L + \left( \frac{\frac{N}{2} - c.f.}{f} \right) h$
$= 35 + \left( \frac{\frac{100}{2} - 36}{25} \right) 10$
$= 35 + \left( \frac{50 - 36}{25} \right) 10$
$= 35 + (14) \frac{10}{25}$
$= 35 + \frac{140}{25}$
$= 35 + 5.6$
$= 40.6$$\therefore$ Median of size of farm is 40.6 acres.