Stem and Leaf Display

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Stem and Leaf Display - short version

This chart displays the frequency distribution by splitting the data values (the last digit in the value) and stems (the remaining digits in the value).

Stem and Leaf Display - long version

A stem-and-leaf display or a stemplot, 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. Stemplots became more commonly used in the 1980s after the publication of John Tukey's publication of Exploratory Data Analysis in 1977. The popularity during those years is attributable to their use of monospaced (typewriter) typestyles that allowed computer technology of the time to easily produce the graphics. Modern computers' superior graphic capabilities have meant these techniques are less often used.

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.

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, often with perfect integrity. They are also useful for highlighting outliers and finding the mode. However, stem and leaf plots are only useful for moderately sized data sets (around 15-150 data points). With very small data sets a stem and leaf plot 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.



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