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 bins.

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.

Superimposed frequency polygons are easier to distinguish than histograms when two or more groups are to be compared. The rectangles for any bin in the different histograms will be identical when their bin frequencies are the same, but the counts in two adjacent bins must be the same for any frequency polygon lines to be identical.

The histograms below show the distributions of marks in two different classes. Again drag the slider to change the histograms into frequency polygons.

It is easier to see that the class represented in red has performed a bit better the class represented in blue when frequency polygons are used.