Question

The following is the distribution of height of students of a certain class in a certain city:

Height (in cms):	160-162	163-165	166-168	169-171	172-174
No. of students:	$15$	$118$	$142$	$127$	$18$

Find the median height.

Answer 1

Class interval ( Exclusive )	Class interval ( Inclusive )	Class interval Frequency	Cumulative Frequency
$160-162$	$159.5-162.5$	$15$	$15$
$163-165$	$162.5-165.5$	$118$	$133$ ( F )
$166-168$	$165.5-168.5$	$142$ (f)	$275$
$169-171$	$168.5-171.5$	$127$	$402$
$172-174$	$171.5-174.5$	$18$	$420$
		$N=420$

We have, $N=420$.

Then, $\frac{N}{2}=\frac{420}{2}=210$

The cumulative frequency just greater than $\frac{N}{2}$ is $275$ then

$165.5-168.5$ is the median class such that, $L=165.5,f=142,F=133$ and $h=168.5-165.5=3$

$\Rightarrow$ $Median=L+\frac{\frac{N}{2}-F}{f}\times h$

$Median=165.5+\frac{210-133}{142}\times h$

$Median=165.5+1.63$

$\therefore$ $Median=167.13$