Other displays of density

A few other graphical displays are sometimes encountered that can look smoother than histograms. The simplest is a frequency polygon which simply joins the midpoints of all histogram classes.

In the diagram below, drag the slider to change the histogram into a frequency polygon.

The frequency polygon is a little smoother (less blocky) than the histogram.

Note that the frequency polygon begins on the horizontal axis (zero height) at the midpoint of the empty class immediately to the left of the histogram and ends on the horizontal axis at the midpoint of the first empty class to the right of the histogram.

Frequency polygons to compare groups

Two or more histograms are sometimes drawn on the same axes to compare groups but careful colouring is needed to distinguish them since parts of the histogram outlines often coincide.

When two or more are superimposed, frequency polygons are easier to distinguish than histograms.

The lines in frequency polygons coincide less often than those in histograms.

Coyote lengths

The histograms below show the lengths (cm) of male and female coyotes that were captured in Nova Scotia. (The blue histogram shows the lengths of the female coyotes and the red histogram shows the males.)

Again drag the slider to change the histograms into frequency polygons.

The two distributions are easier to distinguish when frequency polygons are used. Observe that the two distributions overlap considerably but the male coyotes tend to be slightly longer.