Question

The following is the distribution of the size of certain farms from a taluka (tehasil). Find median size of farms.

Size of Farms(in acres)	Number of Farms
$5-15$	$7$
$15-25$	$12$
$25-35$	$17$
$35-45$	$25$
$45-55$	$31$
$55-65$	$5$
$65-75$	$3$

Answer 1

Size of Farms(in acres)	Number of Farms	Cumulative Frequency
$5-15$	$7$	$7$
$15-25$	$12$	$19$
$25-35$	$17$	$36$
$35-45$	$25$	$61$
$45-55$	$31$	$92$
$55-65$	$5$	$97$
$65-75$	$3$	$100$

$n=\sum f=100$

$\frac{n}{2}=\frac{100}{2}=50$

Therefore, median class $=35-45$, $h=10$

Frequency preceding to the median class $cf=36$

Frequency of the median class $f=25$

Median $=L+\frac{h}{f}(\frac{n}{2}-cf)$

$=35+\frac{10}{25}(50-36)$

$=35+5.6$

$=40.6$