# Cumulative Frequency Distribution and Polygon (2012)

### Introduction to Cumulative Frequency Distribution

A cumulative frequency distribution (cumulative frequency curve or ogive) and a cumulative frequency polygon require cumulative frequencies. The cumulative frequency is denoted by CF and for a class interval it is obtained by adding the frequency of all the preceding classes including that class. It indicates the total number of values less than or equal to the upper limit of that class. For comparing two or more distributions, relative cumulative frequencies or percentage cumulative frequencies are computed.

The relative cumulative frequencies are the proportions of the cumulative frequency denoted by CRF and are obtained by dividing the cumulative frequency by the total frequency (Total number of Observations). The CRF of a class can also be obtained by adding the relative frequencies (rf) of the preceding classes including that class. Multiplying the relative frequencies by 100 gives the corresponding percentage cumulative frequency of a class.

### Method of Construction of Cumulative Frequencies

The method of construction of cumulative frequencies and cumulative relative frequencies is explained in the following table:

### Plot a Cumulative Frequency Distribution

To plot a CF distribution, scale the upper limit of each class along the x-axis and the corresponding cumulative frequencies along the y-axis. For additional information, you can label the vertical axis on the left in units and the vertical axis on the right in percent. The cumulative frequencies are plotted along the y-axis against upper or lower-class boundaries and the plotted points are joined by a straight line. Cumulative Frequency Polygon can be used to calculate median, quartiles, deciles, and percentiles, etc.

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