Elementary Statistics (1+1)

5.2.5.2. Frequency polygon

A frequency polygon is a graph of frequency distribution. It has more than four sides. It is particularly effective in comparing two or more frequency distributions. There are two ways in which a frequency polygon may be constructed.

1. We may draw a histogram of the given data and then join by straight lines the mid-points of the upper horizontal side of each rectangle with the adjacent ones. The figure so formed is called frequency polygon. It is an accepted practice to close the polygon at both ends of the distribution by extending them to the base line. When this is done two hypothetical classes at each end would have to be included – each with a frequency of zero. This extension is made with the objective of making the area under polygon equal to the area under the corresponding histogram. The readers are advised to follow this practice.

2. Another method of constructing frequency polygon is to take the mid-points of the various class-intervals and then plot the frequency corresponding to each point and to join all these points by straight lines. The figures obtained would exactly be the same as obtained by method No. 1. The only difference is that here we have not to construct a histogram.

By constructing a frequency polygon the value of mode can be easily ascertained. If from the apex of the polygon a perpendicular is drawn on the X-axis, we get the value of mode. Moreover, frequency polygons facilitate comparison of two or more frequency distributions on the same graph.