A graphical method for displaying data that is an alternative to the bar chart for displaying data on a discrete random variable, and an alternative to the histogram as a method of approximating the graph of a probability density function.

Suppose a set of discrete numerical data consists of the observed value x₁ with frequency f₁, the observed value x₂ with frequency f₂, and so on. The frequency polygon consists of the straight line segments joining the points with coordinates (x₁, f₁), (x₂, f₂),⋯. It is conventional to start and finish the polygon on the x-axis at appropriate points.

In the case of grouped numerical data with classes of equal width d, say, the frequency polygon consists of the straight-line segments joining the points with coordinates (x₁, f₁), (x₂, f₂),⋯, (x_n, f_n), where x₁, x₂,⋯, x_n are now the midpoints of the class intervals and f₁, f₂,⋯, f_n are the corresponding class frequencies. The polygon starts at (x₁−d, 0) and finishes at (x_n + d, 0). A suitable change of scale gives the relative frequency polygon. As n increases and d decreases, the relative frequency polygon approaches the graph of the corresponding probability density function.

Frequency polygon. This polygon illustrates the frequencies of the heights of 5  732 Scottish militiamen in 1 817.