Cumulative frequency distribution shows the number of observations which fall below or above in a given class interval. If the number of observations fall below in a given class interval then it is called less than cumulative frequency distribution. On the other hand if the numbers of observations fall above in a given class interval then it is called more than cumulative frequency distribution. The cumulative frequency distribution can be explained with the help of following figure.
In the above figure, the first table (starting from left) shows eight class intervals along with corresponding frequencies. The next two tables show cumulative frequency distribution for the first table. It shows that in case of “less than cumulative frequency distribution”, class intervals are converted to open limit class intervals. For example 6 – 11 is converted to “less than 11.5” because in the cumulative frequency of a class all observations in or below a class is associated with the upper boundary of the class. In less than cumulative frequency C.F is calculated by adding the class frequency and frequencies of all lower classes. For example C.F of “less than 11.5” is calculated by adding 0 with 6. Similarly C.F of “less than 17.5” is calculated by adding 6 with 23 (6 + 23 = 29) and so on.
The third table labeled “more than cumulative frequency” shows observations which fall above in given class interval. In this case C.F is calculated by subtracting the class frequency and frequencies of all lower classes. For example C.F of “11.5 or more is 94 which is calculated by subtracting 6 from 100 (100 – 6 = 94). Similarly C.F of “17.5 or more” is obtained by subtracting 23 from 94 (94 – 23 = 71) and so on.