|
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
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