2.6: Cumulative Frequency Distribution

A cumulative frequency distribution is another type of frequency distribution. Instead of reporting how many data values fall in some classes, it reports how many data values are contained in either that class or any class to its left. Technically, it means the sum of frequencies of the class and all the classes below it in a frequency distribution. A cumulative frequency is calculated by adding the frequency of each class lower than the corresponding class interval or category. In general, a cumulative frequency doesn’t have to include everything less than something. The cumulative frequency distribution table calculators save a lot of time when tabulating the data. It makes calculations easier and leads to the organization of data in seconds.

Consider a frequency distribution of customers who bought cameras at different price ranges. The table shows that three customers bought cameras that cost from 40 to 59 dollars.

To find out how many customers bought cameras that cost less than 60 dollars, calculate the cumulative frequency for the first two classes. It is given by the sum of all the frequencies of the current and the preceding class intervals. 

Similarly, the remaining cumulative frequencies are estimated using the same method.

Note that the upper and the lower class limits of the adjacent classes differ by the value of one. These gaps are bridged by calculating the midpoint of these class limits, resulting in the class boundaries.

Notice that there is a difference of 20 between each class boundary. Therefore, subtract 20 from the first and add 20 to the last class boundaries to obtain the start and endpoints, respectively.