In large data sets, jittering the crosses helps show density

A simple dot plot is often adequate for small data sets. However in larger data sets, the crosses often overlap. Indeed, if several crosses coincide, they become indistinguishable from a single cross, so high density may be obscured.

One solution is to randomly move the crosses perpendicularly to the axis in order to separate them somewhat. This is called jittering the points.

(You should rely on a computer to do the jittering for you, but it could be done by hand by rolling a 6- or 10-sided die for each cross to determine its jittering in millimetres.)

Survival time of businesses

A researcher is interested in how long small businesses stay in operation. As part of the study, 120 businesses that closed down during the previous year were investigated. The last registered director of each company was contacted and asked about how long it had been in business. (The information was obtained from local government sources if nobody from the company could be contacted.)

The dot plot below shows the ages of the companies against a horizontal axis.

Drag the slider to jitter the points. Click the button on the right to change the jittering — i.e. to change the random vertical position of the crosses.

Only enough jittering should be used to separate the high density of crosses — moving the slider about half way is best for the data above. Without jittering, too many crosses overlap to allow us to assess the distribution of values.

Note that the vertical positions of the crosses have no importance — the vertical movement of crosses is 'random' and is only intended to separate overlapping crosses.


An alternative solution to the problem of overlapping crosses will be described on the next page.