Question

The marks obtained by 100 students of a class in an examination are given below.

Mark	No. of Student
0 - 5	2
5 - 10	5
10 - 15	6
15 - 20	8
20 - 25	10
25 - 30	25
30 - 35	20
35 - 40	18
40 - 45	4
45 - 50	2

Draw 'a less than' type cumulative frequency curves (ogive). Hence find the median.

Answer 1

We first prepare the cumulative frequency table by less than method as given below–

Marks	No. of students	Marks less than	Cumulative Frequency
0 - 5	2	5	2
5 - 10	5	10	7
10 - 15	6	15	13
15 - 20	8	20	21
20 - 25	10	25	31
25 - 30	25	30	56
30 - 35	20	35	76
35 - 40	18	40	94
40 - 45	4	45	98
45 - 50	2	50	100

Thus we will plot the points (5, 2), (10, 7), (15, 13), (20, 21), (25, 31), (30, 56), (35, 76), (40, 94), (45, 98) and (50, 100).

∴ From the above ogive, the horizontal line drawn from `("N")/(2)=50` intersects the ogive at a point whose x-coordinate is approximately 28.

∴ Hence, Median≈">≈28.