Which digits should be used for the stems?

Which digits from each number should be used as stems? As a first iteration, aim for approximately 10 classes -- this often results in an effective display of density. Try to satisfy the following guidelines:


In the following exercise, use the guidelines to decide which digits should be used for stems and leaves.

Data set 1

Data set 2

Data set 3

Click with the mouse on the list on the left. (It will be highlighted with a yellow border.) Now use the left- and right-arrow keys on the keyboard to adjust which digits of each number to use as stems.

Repeat with the other lists, then click the button Check Stems to check whether you have found the best stems.

How to draw the stem and leaf plot

In the simplest type of stem and leaf plot, distinct stems within the range of the data define the classes (or 'bins') against which the leaves are stacked.

  1. List vertically the distinct stems within the range of the data.
  2. For each value in the data set, draw its leaf digit to the right of its stem in the list of stems.
  3. If drawing the stem and leaf plot by hand, the leaves against each stem should now be sorted into increasing order. (But in the computer-based exercise below, you can do the sorting as part of step 2.)

The following exercises show the technique.

The list on the left below shows the 20 values of industrial contamination that we examined in earlier sections, with each value split into a stem digit and a leaf digit (and no digits discarded).

Use the mouse to drag each of the leaves from the list to their correct position on the stem and leaf plot on the right. While you are dragging, the correct position (or positions if there is more than one possibility) are highlighted in red to guide you.

The stem and leaf plot shows clearly the separation of the 20 samples into two clusters.


Here is another example; again drag the leaves into position. This time, the correct position for the leaves is not highlighted while you are dragging.

If you have difficulty finding the correct positions for the leaves, click the check box Show Hints to turn on highlighting of the correct positions for the leaves

The following exercises give practice at drawing stem and leaf plots with split stems.

Drag the leaves from the list of values on the left to complete a stem and leaf plot with each stem split into two.

If you have difficulty finding the correct positions for the leaves, click the check box Show Hints to turn on highlighting of the correct positions for the leaves


Finally try building the following stem and leaf plot. Note that the lowest 2 of the 5 repeats of stem '2' are not listed, since the data does not contain values with leaves of 0 to 3 on that stem.

 

Negative values

The same principles are used to create stem and leaf displays of data that contain negative values. The only points to take care over are that

  • Distinct stems of -0 and 0 are required.
  • On negative stems, leaves are ordered with leaf 9 at the left (since this corresponds to the lowest value on the stem).

In the following exercise, you will create a stem and leaf plot of a data set that contains negative values.

Try dragging the leaves into place on the following stem and leaf plot.