Graphical displays of density

Sorting a batch of numbers into order can highlight which ranges of values are most and least common — in other words, the values with highest and lowest density. Density is the key to understanding the distribution of numbers in a batch, but there are better ways to display density than a sorted list.

Dot plots

The simplest graphical display of a batch of numbers is a dot plot. This shows each value as a cross (or dot) against a numerical axis.

Software support time

The sorted list on the left below shows the times (in minutes) for a software company to respond to queries about an accounting package that it sells. The data are also displayed in a dot plot on the right.

Drag with the mouse over values on the list to highlight the corresponding cross in the dot plot. Drag over crosses to highlight the corresponding value in the list.

Observe that when successive values in the list are similar, the corresponding crosses are close together. High density is therefore shown in the dot plot with closely grouped crosses.

Note that the 'gap' in the list between 22 and 48 is clearer in the dot plot.

Two modifications to the basic dot plot make it more effective at displaying density in larger batches of values. These will be described in the following pages.