Chapter 3 · Displaying and Summarizing Quantitative Data

Section 3.2Understanding Stem-and-Leaf Displays

Stem-and-leaf displays give you a compact way to organize and visualize quantitative data while preserving every individual value. In this section, you'll learn how to construct and interpret stem-and-leaf displays to describe the shape, center, and spread of a distribution.

Summary

StemThe leading digit(s) of each data value, listed once in a vertical column.

LeafThe trailing digit of each data value, recorded next to its corresponding stem.

Back-to-back displayPlaces two datasets side by side sharing a common stem, making direct comparison easy.

Data preservationUnlike histograms, stem-and-leaf displays retain every individual data value in the plot.

Stem-and-leaf displays are especially useful for small to medium datasets — they reveal distribution shape while keeping every original value visible and readable.

The Real World Statistics Learning Progression

Each section follows the same learning progression: understand the concept, practice the skill, think like a statistician, then apply your learning to authentic data.

Learn This Section

Whether learning independently or teaching a class, the learning path below is designed to help students master the concepts in this section. Page references correspond to the Real World Statistics instructional system.

Read the sectionRead pages 68–72 to reinforce the concepts introduced in the lesson.

Practice what you've learnedComplete the practice questions on pages 72–73. Check your work using the Answer Key, then review and correct any questions you missed before moving on.

Think like a statisticianExplore Enrichment: Role-Based Statistical Analysis Tasks and the Chapter Dataset to apply statistical thinking in real-world contexts.

Need Extra Support? If you'd like additional guidance while working through the practice questions, explore the Worked Solutions Manual for step-by-step solutions and explanations.

From Learners to Statisticians

Examples of authentic statistical work supported by this section include:

Constructing stem-and-leaf displays from small quantitative datasets to reveal distribution shape while preserving individual values (e.g., quiz scores from a classroom assessment, or sprint times from a physical education class).
Using back-to-back stem-and-leaf displays to compare two groups directly (e.g., test scores before and after an intervention, or response times from two different service teams).
Interpreting stem-and-leaf displays to describe the center, spread, and shape of a distribution and identify any unusual values (e.g., plant growth measurements from a science experiment, or daily step counts from a health study).

You may use these ideas to design your own investigations or explore the Real World Statistics System.

Enrichment: Role-Based Statistical Analysis Tasks

Enrichment tasks place students in the role of a statistician working on real research problems, where they evaluate data, justify decisions, and communicate findings clearly. Each section includes multiple enrichment tasks, including one with a model response that demonstrates statistical reasoning in context, showing how evidence is evaluated, decisions are justified, and conclusions are communicated. This serves as a bridge to working with authentic datasets and independent statistical investigation within each chapter.

Available in the Interactive eBook at the end of the section (page 73) and in the Appendix of the Print Book (page 401).

Teaching with Real World Statistics?

These structured learning paths — including Enrichment tasks and Chapter Datasets — can be adapted or copied directly into Canvas, Google Classroom, Schoology, and other learning management systems to simplify lesson planning and student assignments.

Part of the Real World Statistics instructional system — bringing together print, interactive learning, videos, datasets, enrichment, worked solutions, and teacher resources.