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Relative Frequency Histogram:- It uses the same data. The only difference is that it compares each class-interval with the total number of items i.e. instead of the frequency of each class-interval, their relative frequencies are used. Naturally the vertical axis (i.e. y-axis) uses the relative frequencies in places of frequencies.

In the above case we have

Class-interval

Frequency

Relative frequency

$ 1 - $ 5
$ 6 - $10
$11 - $15
$16 - $20
$21 - $25

6
8
10
3
4

6/31
8/31
10/31
3/31
4/31

The Histogram is same as in above case.

Construction of Histogram when class-intervals are unequal:- In a Histogram, a rectangle is proportional to the frequency of the concern class-interval. Naturally, if the class-intervals are of unequal widths, we have to adjust the heights of the rectangle accordingly. We know that the area of a rectangle = l. h. Now suppose the width ( l ) of a class is double that of a normal class interval, its height and thus the corresponding frequency must be halved. After this precaution has been taken, the construction of the Histogram of classes of unequal intervals is the same as before.

Note :- The smallest class-interval should be assumed to be " NORMAL "

Illustration:- Represent the following data by means of Histogram.

Classes : 11-14  16-19  21-24  26-29  31-39  41-59  61-79

Frequencies :  7   19         27       15        12       12         8


Solution:     Note that class-intervals are unequal and also they
                    are of inclusive type.
                    We have to make them equal and of the exclusive
                    type.

                   Correct factor = ( 16 - 14 ) / 2 = 1. Using it we
                   have

Classes :  10-15  15-20  20-25  25-30  30-40  40-60  60-80

Frequencies :   7     19       27       15       12       12         8

Adjusted Heights :    7    19    27    15    12/2   12/4   12/4
(Frequencies)                                            = 6    = 3    = 3

Index

3.1 Introduction
3.2 Comparison Between Tabular And Diagrammatic Presentation
3.3 Difference Between Diagrams And Graphs
3.4 General Principles Of Constructing Diagrams
3.5 Bar Diagrams
3.6 Pie Chart
3.7 Graphs
3.8 Box and Whiskers

Chapter 4





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