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.

Isometric Strength data

In an ergonomic study involving a group of 41 male students from the University of Hong Kong, each student was asked to exert maximum upward force on a horizontal bar which was close to floor level, with his feet 400mm away from the bar. The force was averaged over a 5-second period is called the 'maximum voluntary isometric strength' (MVIS) and is recorded in kilograms.

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 kg.

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 raw data 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.

Isometric Strength data

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

Guinea Pig Survival

The stem and leaf plot below shows the survival times (in days) of 72 guinea pigs that were injected with tubercle bacilli.

The survival times ranged between 43 and 598 days, 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 '9' that is drawn against the stem '5' and observe that it corresponds to the value 598 days. Drag with the mouse over other leaves and observe how each survival time 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.)

Interpretation

Most survival times are between 40 and 150 days, but a few guinea pigs survive for over a year. They are possibly unaffected by the bacilli.