Chapter 3 · Displaying and Summarizing Quantitative Data

Section 3.1Drawing and Understanding Histograms

Histograms help you visualize the distribution of quantitative data by grouping numerical values into intervals. In this section, you'll learn how to construct and interpret histograms to identify patterns such as shape, center, spread, skewness, and possible outliers.

Summary

HistogramsHelp us visualize quantitative data by grouping values into bins (intervals of equal width).

Touching barsBars in a histogram touch each other, emphasizing the continuity of quantitative data.

Distribution shapeInterpreting histograms helps identify the shape of a distribution — symmetric, skewed, or multimodal.

vs. bar graphsHistograms differ from bar graphs in that they handle continuous quantitative data rather than categorical data.

Histograms are the go-to display for quantitative data — they reveal where values cluster, where gaps exist, and whether the distribution is symmetric or skewed.

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 63–66 to reinforce the concepts introduced in the lesson.

Practice what you've learnedComplete the 3 practice questions on pages 66–67. 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 histograms from quantitative data to reveal how numerical values are distributed (e.g., nightly sleep hours from a student wellness survey, or daily rainfall totals from a local weather station).
Interpreting histograms to describe where data is concentrated and identify patterns in a distribution (e.g., emergency room wait times from a hospital log, or commute times from an employee transportation survey).
Comparing multiple histograms to evaluate differences between populations and support evidence-based conclusions (e.g., monthly household energy use across neighborhoods from a utility study, or response times for two customer service centers from company records).

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 67) 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.