Question

Marks obtained by $50$ students in a unit test are given below:

Marks	0-20	20-40	40-60	60-80	80-100
Numbers of students	6	11	17	12	4

Calculate the median marks.

Answer 1

Marks obtained by $50$ students in a unit test are given below:

Marks	0-20	20-40	40-60	60-80	80-100
Numbers of students	6	11	17	12	4

Cumulative frequency 6 17 34 46 50

Here, $n=50$

Hence, $\frac{n}{2}=\frac{50}{2}=25$

The median class lies in the cumulative frequency value $34$.

Hence, median class is $40-60$.

We know that,

Median, $M=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$

Where, $l\to$ lower limit of the median class

$n\to$ total number of observations $(\sum f)$

$cf\to$ cumulative frequency of the class preceding the median class

$f\to$ frequency of the median class

$h\to$ class width

Here, $l=40,n=50,f=17,cf=17,h=10$

$\therefore M=40+\left[\frac{25-17}{17}\right]\times 10$

$\Rightarrow M=40+\frac{8\times 10}{17}$

$\to M=40+\frac{80}{17}$

$\Rightarrow M=40+4.71$

$\therefore M=44.71$

Hence, the median marks for the given data is $44.71$.