Question

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

Marks	No. of students
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 (orgive). Hence find median

Answer 1

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

Let us now plot the points corresponding to the ordered pairs (5, 2), (10, 7) (15,13), (20, 21), (25,31), (30,56), (35,76), (40,94), (45,98), (50,100). Join all the points by a smooth curve.

Locate `"n"/2 = 100/2 = 50` on Y-axis

From this point draw a line parallel to X-axis cutting the curve at a point. From this point, draw a perpendicular to X-axis. The point of intersection of perpendicular with the X-axis determines the median of the data. Therefore median = 28.8