Question

The lengths of $40$ leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table:

Length (in mm)	Number of leaves
$118-126$ $127-135$ $136-144$ $145-153$ $154-162$ $163-171$ $172-180$	$3$ $5$ $9$ $12$ $5$ $4$ $2$

Find the median length of the leaves.

Answer 1

$CI$	$Frequency$	$c.f$
$117.5-126.5$	$3$	$3$
$126.5-135.5$	$5$	$8$
$135.5-144.5$	$9$	$17$
$144.5-153.5$	$12$	$29$
$153.5-162.5$	$5$	$34$
$162.5-171.5$	$4$	$38$
$171.5-180.5$	$2$	$40$
	$N=40$

$\frac{N}{2}=\frac{40}{2}=20$

$\therefore$ Median class $=144.5-153.5$

$\Rightarrow$ $l=144.5,c.f=17,f=12$ and $h=9$

$\Rightarrow$ $Median=l+\frac{\frac{N}{2}-c.f}{f}\times h$

$=144.5+\frac{20-17}{12}\times 9$

$=144.5+\frac{3}{12}\times 9$

$=144.5+2.25$

$=146.75$