Relative Frequency Histogram: It uses the
same data. The only difference is that it compares each classinterval
with the total number of items i.e. instead of the frequency of
each classinterval, their relative frequencies are used. Naturally
the vertical axis (i.e. yaxis) uses the relative frequencies in
places of frequencies.
In the above case we have
Classinterval 
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 classintervals
are unequal: In a Histogram, a rectangle is proportional to
the frequency of the concern classinterval. Naturally, if the classintervals
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 classinterval should be assumed to be " NORMAL "
Illustration: Represent the following data by means of Histogram.
Classes : 1114 1619 2124 2629 3139 4159 6179
Frequencies : 7 19 27 15 12 12 8
Solution: Note
that classintervals 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 : 1015 1520 2025 2530 3040 4060 6080
Frequencies : 7 19 27 15 12 12 8
Adjusted Heights : 7 19 27 15 12/2 12/4 12/4
(Frequencies) = 6 = 3 = 3
