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Draw the frequency polygon representing the above data without drawing the histogram. Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a highway :
Class interval Frequency
30 - 40 3
40 - 50 6
50 - 60 25
60 - 70 65
70 - 80 50
80 - 90 28
90 - 100 14

Solution:

Given, the table represents the frequency distribution for the speed of cars passing through a particular spot on a highway.

We have to draw a frequency polygon representing the above data without drawing the histogram.

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

Class mark = (30 + 40)/2 = 70/2 = 35

Class interval	Class marks	Frequency
30 - 40	(30 + 40)/2 = 35	3
40 - 50	(40 + 50)/2 = 45	6
50 - 60	(50 + 60)/2 = 55	25
60 - 70	(60 + 70)/2 = 65	65
70 - 80	(70 + 80)/2 = 75	50
80 - 90	(80 + 90)/2 = 85	28
90 - 100	(90 + 100)/2 = 95	14

We can represent the class marks along the horizontal axis.

The corresponding frequencies are represented along the vertical axis.

The points are B(35, 3) C(45, 6) D(55, 25) E(65, 65) F(75, 50) G(85, 28) and H(95, 14)

A frequency polygon is obtained by plotting the given points,

Draw the frequency polygon representing the above data without drawing the histogram. Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a highway : Class interval Frequency 30 - 40 3 40 - 50 6 50 - 60 25 60 - 70 65 70 - 80 50 80 - 90 28 90 - 100 14

Consider the classes 20 - 30 and 100 - 110 each with frequency 0.

The class marks of these classes are 25 and 105 at the points A and l are obtained from the graph.

Join all the points using a dotted line.

Therefore, the curve ABCDEFGHI represents the frequency polygon

✦ Try This: Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a highway :

Class interval	Frequency
30 - 40	5
40 - 50	6
50 - 60	27
60 - 70	67
70 - 80	59
80 - 90	34
90 - 100	19

Draw the frequency polygon representing the above data without drawing the histogram.

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

NCERT Exemplar Class 9 Maths Exercise 14.4 Problem 8

Draw the frequency polygon representing the above data without drawing the histogram. Following table shows a frequency distribution for the speed of cars passing through at a particular spot on a highway : Class interval Frequency 30 - 40 3 40 - 50 6 50 - 60 25 60 - 70 65 70 - 80 50 80 - 90 28 90 - 100 14

Summary:

The table represents the frequency distribution for the speed of cars passing through a particular spot on a highway. A frequency polygon representing the data above is shown in the graph

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