# Basic Statistics and Data Analysis

## Cumulative Frequency Distribution and Polygon

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 distributi0ons, relative cumulative frequencies or percentage cumulative frequencies are computed.

The relative cumulative frequencies are the proportions of the cumulative frequency denoted by crf 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 corresponding percentage cumulative frequency of a class.

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

cumulative frequency distribution

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

Cumulative Frequency Polygon or Ogive