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.