Question

Calculate the median for the following data.

Marks	$20$	$9$	$25$	$50$	$40$	$80$
No. of students	$6$	$4$	$16$	$7$	$8$	$2$

Answer 1

Let us arrange marks in ascending order.

Marks	$f$	$cf$
$9$	$4$	$4$
$20$	$6$	$10$
$25$	$16$	$26$
$40$	$8$	$34$
$50$	$7$	$41$
$80$	$2$	$43$
	$n=43$

Here, $n=43$, which is odd
Position of median $={\left(\frac{n+1}{2}\right)}^{th}$ observation.
$={\left(\frac{43+1}{2}\right)}^{th}$ observation.
$={22}^{nd}$ observation.
The above table shows that all items from ${11}^{th}$ to ${26}^{th}$ have their value $25$. So, the value of ${22}^{nd}$ item is $25$.
$\therefore$ Median $=25$.