Marks obtained by 70 students are given below :

Marks	No. of students
20	8
70	12
50	18
60	6
75	9
90	5
40	12

Calculate the median marks.

On arranging the given variates (marks) in ascending order, we construct the cumulative frequency table as under :

Here, n (total no. of students) = 70, which is even.

$\therefore \text{Median} = \dfrac{\dfrac{n}{2} \text{th observation} + \big(\dfrac{n}{2} + 1\big)\text{ th observation}}{2} \\[1em] = \dfrac{\dfrac{70}{2} \text{th observation} + \big(\dfrac{70}{2} + 1\big)\text{ th observation}}{2} \\[1em] = \dfrac{\text{ 35th observation + 36th observation}}{2} \\[1em]$

All observations from 21st to 38th are equal, each = 50.

Hence, median

$= \dfrac{50 + 50}{2} \\[1em] = \dfrac{100}{2} \\[1em] = 50$

Hence, median marks = 50.