Cumulative Frequency Distribution

Cumulative Frequency Distribution

Cumulative frequency corresponding to a class interval is defined as the total frequency of all values less than upper boundary of the class. A tabular arrangement of all cumulative frequencies together with the corresponding classes is called a cumulative frequency distribution or cumulative frequency table.

The main difference between a frequency distribution and a cumulative frequency distribution is that in the former case a particular class interval according to how many items lie within it is described, whereas in the latter case the number of items that have values either above or below a particular level is described.

There are two forms of cumulative frequency distributions, which are defined as follows:

(i) Less than Cumulative Frequency Distribution: In this type of cumulative frequency distribution, the cumulative frequency for each class shows the number of elements in the data whose magnitudes are less than the upper limit of the respective class.

(ii) More than Cumulative Frequency Distribution: In this type of cumulative frequency distribution, the cumulative frequency for each class shows the number of elements in the data whose magnitudes are larger than the lower limit of the class.

Example 3.15

Construct less than and more than cumulative frequency distribution tables for the following frequency distribution of orders received by a business firm over a number of weeks during a year.

Solution: 

For the data related to the number of orders received per week by a business firm during a period of one year, the less than and more than cumulative frequencies are computed and are given in Table 3.15

Relative-Cumulative Frequency Distributions

The relative cumulative frequency is defined as the ratio of the cumulative frequency to the total frequency. The relative cumulative frequency is usually expressed in terms of a percentage. The arrangement of relative cumulative frequencies against the respective class boundaries is termed as relative cumulative frequency distribution or percentage cumulative frequency distribution.

Example 3.16

For the data given in Example 3.15 find the relative cumulative frequencies.

Solution:

For the data given in Example 3.15 the less-than and more-than cumulative frequencies are obtained and given in Table 3.15 The relative cumulative frequency is computed for each class by dividing the respective class cumulative frequency by the total frequency and is expressed as a percentage. The cumulative frequencies and related cumulative frequencies are tabulated in Table 3.16