Question

Distribution of marks obtained by 100 students of a class is given below. Find out the median marks.

Marks	0	5	10	15	20	25	30	35	40	45
Number of Students	4	6	15	5	8	12	28	14	3	5

Answer 1

Marks	No. of Student (f)	Cumulative Frequency (c.f.)
0	4	4
5	6	10
10	15	25
15	5	30
20	8	38
25	12	50
30	28	78
35	14	92
40	3	95
45	5	100
	N = 100

Median = size of ${\left(\frac{N+1}{2}\right)}^{th}$item
or, Median = size of ${\left(\frac{100+1}{2}\right)}^{th}$ item
or, Median = size of 50.5^th item
Now, we need to locate this item in the column of Cumulative Frequency. The item just exceeding 50.5^th is 78 (in the c.f. column), which is corresponding to 30.
Hence, median is 30.