Question

The hearts of $60$ patients were examined through X-ray and the observations obtained are given. Find the median.

Diameter of heart(in mm)	$130$	$131$	$132$	$133$	$134$	$135$
Number of patients	$7$	$9$	$15$	$12$	$6$	$11$

Answer 1

Diameter of heart (in mm)	Number of patients	$cf$
$130$	$7$	$7$
$131$	$9$	$16$
$132$	$15$	$31$
$133$	$12$	$43$
$134$	$6$	$49$
$135$	$11$	$60$
Total	$60$

Here, $N=60$ (even)

So, Median $M=\frac{(N/2{)}^{th}\text{observation}+(N/2+1{)}^{th}\text{observation}}{2}$

$M=\frac{{30}^{th}\text{observation}+{31}^{th}observation}{2}$

$\Rightarrow M=\frac{132+132}{2}=132$ (Here, $30$ and $31$ both lies in the cumulative frequency $31$, so corresponding observation for both is $132$)

Hence, the median is $132$