Stem-and-leaf display

stemplot primes

Stem leaf plot 001

Stem-and-leaf display is a graphical method used in statistics to present quantitative data in a compact form. This method is particularly useful for displaying the distribution of a dataset. The stem-and-leaf display was popularized by John Tukey in the 1970s as a quick way to visualize the shape of a distribution, similar to a histogram, but with the added benefit of retaining the actual data values.

Overview

A stem-and-leaf display consists of two parts: the "stem," which represents the leading digits of the data points, and the "leaf," which represents the trailing digits. The stems are listed in a vertical column, usually in ascending order, and the leaves that correspond to each stem are listed on the right side of the stem. This method allows for the data to be sorted into groups (the stems) and provides a quick visual representation of the distribution of the data.

Construction

To construct a stem-and-leaf display, one must first decide on the stem unit, which could be tens, hundreds, etc., depending on the range of the data. The leaf unit is then typically the next smallest unit. For example, if the data range from 32 to 78, the stem unit might be tens, and the leaf unit would be ones. Each data point is then split into a stem and a leaf, with the stem being the integer part of the data point divided by the leaf unit, and the leaf being the remainder.

Example

Consider the following dataset: 34, 36, 40, 45, 47, 50.

A stem-and-leaf display for this data would look like this:

3 | 4 6 4 | 0 5 7 5 | 0

In this example, the tens place is used as the stem, and the ones place is used as the leaf. This display shows that there are two data points in the 30s, three in the 40s, and one in the 50s.

Advantages and Disadvantages

The main advantage of a stem-and-leaf display is its ability to show the distribution of a dataset while preserving the original data points. This can be particularly useful for small to medium-sized datasets and for preliminary data analysis. It also allows for easy comparison of two or more distributions.

However, stem-and-leaf displays have limitations. They are not well-suited for large datasets because the display can become unwieldy. Additionally, they are not ideal for datasets with a large range of values or for data that do not have a simple decimal base.

Applications

Stem-and-leaf displays are used in various fields, including education, where they serve as a teaching tool to introduce students to statistical distribution, and in data analysis, where they provide a quick overview of the distribution of a dataset. They are particularly favored in exploratory data analysis, where understanding the shape and spread of the data is more important than detailed statistical analysis.