Question

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

Marks	Number 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 cumulative frequency curves by using (i) ‘less than’ series and (ii) ‘more than’ series.Hence, find the median.

Answer 1

(i) From the given table, we may prepare the ‘less than’ frequency table as shown below:

Marks	Number of students
Less than 5	2
Less than 10	7
Less than 15	13
Less than 20	21
Less than 25	31
Less than 30	56
Less than 35	76
Less than 40	94
Less than 45	98
Less than 50	100

We plot the points A(5, 2), B(10, 7), C(15, 13), D(20, 21), E(25, 31), F(30, 56), G(35, 76) and H(40, 94), I(45, 98) and J(50, 100).
Join AB, BC, CD, DE, EF, FG, GH, HI, IJ and JA with a free hand to get the curve  representing the ‘less than type’ series.
(ii) More than series:

Marks	Number of students
More than 0	100
More than 5	98
More than 10	93
More than 15	87
More than 20	79
More than 25	69
More than 30	44
More than 35	24
More than 40	6
More than 45	2

Now, on the same graph paper, we plot the points (0, 100), (5, 98), (10, 94), (15, 76), (20, 56), (25, 31), (30, 21), (35, 13), (40, 6) and (45, 2). Join with a free hand to get the ‘more than type’ series.

The two curves intersect at point L. Draw LM ⊥ OX cutting the x-axis at M.
Clearly, M = 29.5
Hence, Median = 29.5