Table of Contents
What Is a Stem-and-Leaf Plot?
A stem-and-leaf plot (or stemplot) is a technique for presenting quantitative data in a visual format similar to a histogram but preserving the original data values. Each number is split into a stem (all digits except the last) and a leaf (the last digit). The stems are listed vertically, and leaves are listed horizontally, creating a display that shows the distribution shape.
Invented by John Tukey in the 1970s as part of exploratory data analysis, stem-and-leaf plots are particularly useful for small to medium datasets (up to about 100 values). They allow you to see the distribution shape, identify clusters and gaps, spot outliers, and read off the actual data values all from a single display.
How to Read It
Each row shows a stem on the left of the vertical bar and leaves on the right. For example, the row "3 | 1 3 4" represents the values 31, 33, and 34. The number of leaves in each row shows the frequency for that stem range, making the plot act like a horizontal histogram.
Advantages Over Histograms
- Preserves all original data values (no information loss)
- Easy to construct by hand for small datasets
- Shows the overall shape of the distribution
- Allows easy identification of the median and quartiles
- Reveals clusters, gaps, and outliers
Frequently Asked Questions
How do I handle negative numbers?
Negative numbers use a negative stem. For example, -23 has stem -2 and leaf 3. List negative stems in descending order above zero, then positive stems in ascending order below.
When should I use a stem-and-leaf plot vs a histogram?
Use stem-and-leaf plots for small datasets (n less than 100) when you want to preserve individual values. Use histograms for larger datasets where individual values are less important than the overall shape and where stem-and-leaf plots would be too long to display clearly.