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Following table gives the distribution of students of sections A and B of a class according to the marks obtained by them.
Section A Section B
Marks Frequency Marks Frequency
0 - 15 5 0 - 15 3
15 - 30 12 15 - 30 16
30 - 45 28 30 - 45 25
45 - 60 30 45 - 60 27
60 - 75 35 60 - 75 40
75 - 90 13 75 - 90 10
Represent the marks of the students of both the sections on the same graph by two frequency polygons.What do you observe?

Solution:

Given, the table represents the frequency distribution of students of sections A and B of a class according to the marks obtained by them.

We have to represent the marks of the students of both the sections on the same graph by two frequency polygons.

histogram.

To draw a frequency polygon, first we have to find the mid marks

Mid marks = (0 + 15)/2 = 15/2 = 7.5

Section A			Section B
Marks	Mid marks	Frequency	Marks	Mid marks	Frequency
0 - 15	(0 + 15)/2 = 7.5	5	0 - 15	(0 + 15)/2 = 7.5	3
15 - 30	(15 + 30)/2 = 22.5	12	15 - 30	(15 + 30)/2 = 22.5	16
30 - 45	(30 + 45)/2 = 37.5	28	30 - 45	(30 + 45)/2 = 37.5	25
45 - 60	(45 + 60)/2 = 52.5	30	45 - 60	(45 + 60)/2 = 52.5	27
60 - 75	(60 + 75)/2 = 67.5	35	60 - 75	(60 + 75)/2 = 67.5	40
75 - 90	(75 + 90)/2 = 82.5	13	75 - 90	(75 + 90)/2 = 82.5	10

We can represent the class marks along the horizontal axis.

The corresponding frequencies are represented along the vertical axis.

For section A,

The points are A(7.5, 5) B(22.5, 12) C(37.5, 28) D(52.5, 30) E(67.5, 35) F(82.5, 13)

For section B,

The points are H(7.5, 3) I(22.5, 16) J(37.5, 25) K(52.5, 27) L(67.5, 40) M(82.5, 10)

Plot the points on the graph and join all the points.

From the frequency polygon of two sections we observe that maximum marks of 67.5 is scored by 40 students of section B.

✦ Try This: Following table gives the distribution of students of sections A and B of a class according to the marks obtained by them.

Section A		Section B
Marks	Frequency	Marks	Frequency
0 - 15	3	0 - 15	7
15 - 30	9	15 - 30	6
30 - 45	17	30 - 45	35
45 - 60	5	45 - 60	27
60 - 75	25	60 - 75	50
75 - 90	18	75 - 90	56

Represent the marks of the students of both the sections on the same graph by two frequency polygons.What do you observe?

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 14

NCERT Exemplar Class 9 Maths Exercise 14.4 Problem 9

Following table gives the distribution of students of sections A and B of a class according to the marks obtained by them. Section A Section B Marks Frequency Marks Frequency 0 - 15 5 0 - 15 3 15 - 30 12 15 - 30 16 30 - 45 28 30 - 45 25 45 - 60 30 45 - 60 27 60 - 75 35 60 - 75 40 75 - 90 13 75 - 90 10. Represent the marks of the students of both the sections on the same graph by two frequency polygons.What do you observe?

Summary:

The table represents the frequency distribution of students of sections A and B of a class according to the marks obtained by them. On representing the marks of the students of both the sections on the same graph by two frequency polygons, we observe that a maximum of 67.5 marks is obtained by 40 students of section B

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