Value of stem and leaf plots

Although a stem and leaf plot contains more detail about the values than the corresponding stacked dot plot, this extra information rarely helps you to understand the data.

Project marks

One situation in which the author has found stem and leaf plots useful is to show the distribution of marks to students. The stem and leaf plot below shows the marks that students attained in a recent statistics project that was marked out of 60.

The stem and leaf plot shows the distribution of marks well, but also allows any student to determine exactly his/her place in the class. For example, a student who got 57/60 can easily count that 7 students got a higher mark in the class.

In most situations however, stem and leaf plots have few advantages over stacked dot plots as graphical displays of data.

Drawing a stem and leaf plot by hand

Stem and leaf plots are mostly used because they are easy
to draw by hand. |

We now explain how to draw a stem and leaf plot with pencil and paper.

Identify the stem and leaf digits

The most significant digits of any value are its **stem**, the
next digit is called its **leaf** and any further less significant
digits are discarded.

The position of the leaf digits should usually be done to give between 10 and 20 distinct stems. If this is not possible, the stems can be split to give this number of classes for the plot.

Examples

Drag the slider to split each value in the list into a stem and a leaf digit.

Use the pop-up menu to see how other values might be split into stems and leaves. Observe that:

- In the data set
**Multi-digit stems**, the decimal point is not included in the stems. The position of the decimal point is indicated by key that must be drawn at the top of the stem and leaf plot. - In the data set
**Values that must be truncated**, some digits from each value are ignored. Note that the values are truncated, not rounded. Note also that the leading zeros are removed from the stems.

Drawing the stem and leaf plot

After identifying the stems and leaf digits for the values:

- Write stems in a column
- All possible distinct stems within the range of the data should be written down. If a split stem and leaf plot is to be drawn, each stem should be repeated 2 or 5 times. The stems can be ordered with either the highest or lowest stem at the top, but be consistent.
- Add the leaves
- Scan through all data values, writing the leaf digits in rows against the corresponding stems. This can be done quickly by hand.
- Sort the leaves
- Sort the leaves against each stem into increasing order. This final step may be omitted for a quick look at the distribution of values.

Example

The example below illustrates the process of constructing a stem and leaf plot from a list of values (on the right below).

Click on the first value. The digits to the left of the decimal point identify the value's stem and its 'tenths' digit is written against it. Continue clicking the values in the list to build up the stem and leaf plot.

Finally, click **Sort Leaves** to sort the leaves into order on
each stem.

Guinea Pig Survival

Our final example shows how a split stem and leaf plot for the guinea pig survival data on the previous page is drawn. The data set is presented on the right as a sorted list, so the final step of sorting the leaves is unnecessary if the values are added in order.

Again, click the values to split them into stems and leaves and add the leaves to the plot. Note that the 'units' digits of the values are ignored.