Stemplot

A stemplot (or stem-and-leaf plot), in statistics, is a device for presenting quantitative data in a graphical format, similar to a histogram, to assist in visualizing the shape of a distribution. They evolved from Arthur Bowley's work in the early 1900s, and are useful tools in exploratory data analysis.

Unlike histograms, stemplots retain the original data to at least two significant digits, and put the data in order, thereby easing the move to order-based inference and non-parametric statistics.

A basic stemplot contains two columns separated by a vertical line. The left column contains the "stems" and the right column contains the "leaves".

Constructing a stemplot

To construct a stemplot, the observations must first be sorted in ascending order. Here is the sorted set of data values that will be used in the following example: 44 46 47 49 63 64 66 68 68 72 72 75 76 81 84 88 106Next, it must be determined what the stems will represent and what the leaves will represent. Typically, the leaf contains the last digit of the number and the stem contains all of the other digits. In the case of very large or very small numbers, the data values may be rounded to a particular place value (such as the hundreds place) that will be used for the leaves. The remaining digits to the left of the rounded place value are used as the stems.

In this example, the leaf represents the ones place and the stem will represent the rest of the number (tens place and higher).

The stemplot is drawn with two columns separated by a vertical line. The stems are listed to the left of the vertical line. It is important that each stem is listed only once and that no numbers are skipped, even if it means that some stems have no leaves. The leaves are listed in increasing order in a row to the right of each stem. 4 | 4 6 7 9 5
6 | 3 4 6 8 8 7 | 2 2 5 6 8 | 1 4 8 9 | 10 | 6 key: 5|4=54 leaf unit: 1.0 stem unit: 10.0

For negative numbers, a negative is placed in front of the stem unit, which is still the value X / 10. Non-integers are rounded. This allowed the stem and leaf plot to retain its shape, even for more complicated data sets. As in this example below: -2 | 4 -1 | 2 -0 | 3 0 | 4 6 6 1 | 7 2 | 5 3 | 4 | 5 | 7

Which, with rounding to the nearest unit, represents the set of data: -23.678758, -12.45, -3.4, 4.43, 5.5, 5.678, 16.87, 24.7, 56.8

Usage

Stemplots are useful for displaying the relative density and shape of the data, giving the reader a quick overview of distribution. They retain most of the raw numerical data, in some cases with perfect integrity. They are also useful for highlighting outliers and finding the mode. However, stemplots are only useful for moderately sized data sets (around 15-150 data points). With very small data sets a stemplot can be of little use, as a reasonable number of data points are required to establish definitive distribution properties. A dot plot may be better suited for such data. With very large data sets, a stemplot will become very cluttered, since each data point must be represented numerically. A box plot or histogram may become more appropriate as the data size increases.

The ease with which histograms can now be generated on computers has meant that stemplots are less used today than in the 1980s, when they first became widely utilized as a quick method of displaying information graphically by hand.

References

*Wild, C. and Seber, G. (2000) "Chance Encounters: A First Course in Data Analysis and Inference" pp. 49-54 John Wiley and Sons. ISBN 0-471-32936-3