Box plots cannot show clusters

 

Eruptions of Old Faithful Geyser

Use the slider in the top diagram to change the data set into one with two clusters. Point out that the box plot cannot show the gap (low density of values) in the middle.

(You could mention that the closeness of the quartiles and extremes does give a hint that there could be a gap in the middle of the distribution.)

The second diagram is a static example of a real data set with clusters.

The Old Faithful Geyser in the Yellowstone National Park in the USA erupts regularly. The dot plot shows the durations of these eruptions in October 1980.

The box plot hides the fact that there are two types of eruption.