Cumulative frequency refers to the total frequency of a given class and all prior classes in a graph. For example, say that you have researched the price of gas at several gas stations in your area, and you broke down the price ranges into classes. Using a class range of $0.25, you might find results similar to those in the first two columns of the following table.
Now, say you wanted to find out the cumulative frequencies for the gas station data. To figure out the cumulative frequency of each class, you simply add its frequency to the frequency of the previous class.
| Gas Prices ($/Gallon) |
Number of Gas Stations | Cumulative Frequency | Cumulative Frequency (percent) |
|---|---|---|---|
| $3.50–$3.74 | 6 | 6 | 30% |
| $3.75–$3.99 | 4 | 6 + 4 = 10 | 50% |
| $4.00–$4.24 | 5 | 6 + 4 + 5 = 15 | 75% |
| $4.25–$4.49 | 5 | 6 + 4 + 5 + 5 = 20 | 100% |
In this example, for the $3.75 to $3.99 class, you add its class frequency (4) to the frequency of the previous class ($3.50 to $3.74, which is 6), so 6+4 = 10. This result shows you that ten gas stations' prices are between $3.50 and $3.99. Because 20 gas stations were used in the sample, the percentage of all gas stations with prices between $3.50 and $3.99 is 10/20 or 50 percent of the total.
