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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 the distribution of the data is normal, then the ogive represents what is popularly known as a bell curve or a normal distribution.
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