Stem-and-Leaf Data Visualization

Aug 21, 2025

Overview

This lecture explains how to construct and interpret stem-and-leaf displays, a graphical method for summarizing numerical data, including variations for different data types and comparison purposes.

Constructing a Stem-and-Leaf Display

  • A stem-and-leaf display organizes data by splitting numbers into "stems" (left, higher place value) and "leaves" (right, lower place value).
  • Stems typically represent the tens digit; leaves are the ones digit (e.g., stem 3 with leaf 2 represents 32).
  • To create the display, list all stems in order, then list leaves in order next to each stem.
  • Each data point is represented by adding leaf value to ten times its stem.

Interpreting the Display

  • The shape of the stem-and-leaf plot shows the distribution of data, revealing clusters, gaps, and outliers more clearly than raw numbers.
  • Longer rows indicate more frequent values; the precise data can be read by combining stem and leaf values.

Variations and Refinements

  • Stems can be split into finer intervals if rows are too long (e.g., 30–34 and 35–39).
  • Each split reveals more detailed grouping of data and a clearer distribution.
  • Use judgment to decide how many splits make sense for your data set.

Back-to-Back Stem-and-Leaf Plots

  • A back-to-back display compares two data sets using shared stems in the center and leaves branching left and right.
  • Useful for comparing distributions across two groups or time periods.

Special Data Considerations

  • Works best for whole numbers and small datasets (less than about 200 observations).
  • For more digits or decimals, round numbers so that stems and leaves each represent one digit.
  • Negative numbers use negative stems; zero can be represented with both zero and negative zero stems for values just above/below zero.
  • Stems and leaves can represent larger units (like 100,000 and 10,000) for bigger numbers.

Deciding When to Use a Stem-and-Leaf Display

  • Appropriate when the data can be meaningfully rounded to two digits and all values fit within the chosen stem/leaf format.
  • Consider alternative graphs if rounding causes significant information loss or if the data set is very large.

Key Terms & Definitions

  • Stem — The left part of a number in a stem-and-leaf plot, usually representing a higher place value (e.g., tens, hundreds).
  • Leaf — The rightmost digit of a number in the display, representing the smallest place value being plotted.
  • Back-to-Back Plot — A stem-and-leaf plot with stems in the center and two sets of leaves on either side for comparing two groups.

Action Items / Next Steps

  • Practice constructing stem-and-leaf plots with sample data sets.
  • Read the textbook section on stem-and-leaf displays and their variations.