Frequency Curves
At many times we are interested in knowing 'How many workers of a factory earn less than $ 700 per month' or 'percentage of students who have failed', or 'How many workers earn more than $1, 000 per month' etc. To answer these questions, it is necessary to add the frequencies. When frequencies are added, they are known as cumulative frequencies. These frequencies are then listed in a table known as the cumulative frequency table. The curve obtained by plotting cumulative frequencies is known as the cumulative frequency curve of an ogive (pronounced olive).
There are two methods of constructing an ogive, namely:
(a) The less than method and
(b) The more than method
(a) Less than method: In the less than method we start with the upper limits of the classes and on adding the frequencies. Whenever these frequencies are plotted we get a rising curve.
(b) More than method: In the more than method we start with the lower limits of the classes and from the frequencies we subtract the frequency of every class. Whenever these frequencies are plotted we get a declining curve.
The following frequency distribution is converted into a cumulative frequency distribution, at first by the less than method and then by the more than method.
|
marks
|
No. of students
|
marks
|
No. of students
|
|
10-20
|
4
|
40-50
|
20
|
|
20-30
|
6
|
50-60
|
18
|
|
30-40
|
|
60-70
|
2
|
Cumulative frequency distributions
|
Marks less than
|
No. of students
|
Marks more than
|
No. of students
|
|
20
|
4
|
10
|
60
|
|
30
|
10
|
20
|
56
|
|
40
|
20
|
30
|
50
|
|
50
|
40
|
40
|
40
|
|
60
|
58
|
50
|
20
|
|
70
|
60
|
60
|
2
|
|
|
|
70
|
0
|