Question

The scores obtained by $50$ students in an examination is tabulated as shown below.

Score	Number of students
below $10$	$3$
below $20$	$7$
below $30$	$13$
below $40$	$22$
below $50$	$32$
below $60$	$40$
below $70$	$46$
below $80$	$50$

Find the median score.

Answer 1

Score	Number of Students
Below $10$	$3$
Below $20$	$7$
Below $30$	$13$
Below $40$	$22$
Below $50$	$32$
Below $60$	$40$
Below $70$	$46$
Below $80$	$50$

Here median score is the score $x$ for which the number of students is $\frac{50}{2}=25$
The number of students $y=25$ occurs between the number of students $y=22$ having score $x=40$ and the number of students $y=32$ having score $x=50$ in the table.
So using proportionality assumption,
$\frac{x-40}{50-40}=\frac{25-22}{32-22}$
$x-40=3$
$x=43$
This means that the median score is $43$.