Too many or too few stems

Sometimes a basic stem and leaf plot has only between 2 and 5 distinct stems. Changing the stem units would give between 20 and 50 stems — too many classes to clearly show the density of values by the heights of the stacks of leaves.

Students failing arithmetic exam

All children in a country sit a national arithmetic and language exam at the end of the year in which they leave primary school. The two stem and leaf plots below show the percentage of students failing the arithmetic exam in 2007 from each of the 41 primary schools in a region. Each 'leaf' represents the failure rate for one of these schools.

With the leaves as the 'units' digits, most values are stacked on stems '1' and '2'. The stem and leaf plot does not show the shape of the distribution well within the interval 10 to 29 percent.

However making the leaves the 'tenths' digits results in too many distinct stems for a data set of this size.

The stem and leaf plot is rather jagged. Also, all leaves are '0' since the percentages were recorded as whole numbers, so there is no advantage over a stacked dot plot.

Extra flexibility

It is possible to extend the basic stem and leaf plot to display an intermediate number of classes (stacks of leaves).

Each distinct stem from the basic plot can be split into either 2 or 5 different classes.

This increases the number of stems by a factor or either 2 or 5.

Again the idea is explained more clearly with an example than in words.

Students failing arithmetic exam

Click on the Animate button to see the stems split into two. Note the leaves that end on each stem. The slider can be used to repeat the animation more slowly.

Select Split into 5 from the pop-up menu, then repeat the animation.

Another example

Storm duration

In a detailed hydrological study in Malawi, rainfall data were collected from a continuously recording rain gauge installed in Bvumbwe catchment. The durations (minutes) of the first 50 storms in the 1983/4 rainy season are shown below.

The durations ranged between 5 and 885 minutes, so the stems are hundreds and each leaf is the 'tens' digit of a value. Note that the 'units' digits of the values are not shown on the stem and leaf plot.

The stem and leaf provide the most significant digits of each value.

Click on the top leaf of '8' that is drawn against the stem '8' and observe that it corresponds to the value 885 days. Drag with the mouse over other leaves and observe how each storm duration is represented in the diagram.

(You may notice that the values are not rounded to the nearest leaf digit, but are truncated. This is done to simplify drawing the plot by hand and should not affect your interpretation of the plot.)

Most storms last between 0 and 200 minutes, but a few are much longer.