Stem-and-leaf display

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Time table using a stem-and-leaf layout at Minato Mirai train station in Yokohama, Japan. It is a widespread design pattern in the country.

A stem-and-leaf display 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 book on exploratory data analysis in 1977.[1] 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.

A stem-and-leaf display is often called a stemplot, but the latter term often refers to another chart type.[2] A simple stem plot may refer to plotting a matrix of y values onto a common x axis, and identifying the common x value with a vertical line, and the individual y values with symbols on the line.

Unlike histograms, stem-and-leaf displays 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 stem-and-leaf display contains two columns separated by a vertical line. The left column contains the stems and the right column contains the leaves.

Usage[edit]

Stem-and-leaf displays 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 displays are only useful for moderately sized data sets (around 15-150 data points). With very small data sets a stem-and-leaf displays 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 stem-and-leaf display 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 stem-and-leaf displays are less used today than in the 1980s, when they first became widely utilized as a quick method of displaying information graphically by hand.

Notes[edit]

  1. ^ Tukey, John W. (1977). Exploratory Data Analysis (1 ed.). Pearson. ISBN 0-201-07616-0. 
  2. ^ For example, MATLAB's and Matplotlib's stem functions, do not create a stem-and-leaf display.

References[edit]