## Cumulative Frequency Distribution and Polygon

A * cumulative frequency distribution* (

*or*

**cumulative frequency curve***and a*

**ogive)***require*

**cumulative frequency polygon***. The*

**cumulative frequencies***is denoted by*

**cumulative frequency***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:

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.

*can be used to calculate*

**Cumulative Frequency Polygon***median, quartiles, deciles*and

*percentiles*etc.