Cumulative Frequency Distribution

Once a frequency distribution has been created and the data are visually represented by means of a histogram or a frequency polygon, another option is to create a cumulative frequency distribution, or a visual representation of the cumulative frequency of occurrences by class intervals.

A cumulative frequency distribution is based on the same data as a frequency distribution, but with an added column (cumulative frequency), as shown in Table 1.

Table 1 Cumulative Frequency Distribution
Class Interval	Frequency	Cumulative Frequency
65–69	1	40
60–64	4	39
55–59	5	35
50–54	4	30
45–49	3	26
40–44	5	23
35–39	6	18
30–34	5	12
25–29	4	7
19–24	3	3

The cumulative frequency distribution begins by the creation of a new column labeled “Cumulative frequency.” Then, the frequency in each class interval is added to all the frequencies below it. For example, for the class interval of 19–24, there are 3 occurrences and none below it, so its cumulative frequency is 3. For the class interval of 25–29, there are 4 occurrences and 3 below it, for a total of 7 (4 + 3) occurrences in that class interval or below it. The last class interval (65–69) contains 1 occurrence, and there is a total of 49 occurrences at or below that class interval.

Once the cumulative frequency distribution is created, the data can be plotted just as they were for a histogram or a frequency polygon. Another name for a cumulative frequency polygon is an ogive. And if[Page 206] the distribution of the data is normal, then the ogive represents what is popularly known as a bell curve or a normal distribution.