Chapter 2 · Displaying and Summarizing Categorical Data

Section 2.3Drawing and Interpreting Bar Graphs

Bar graphs help you organize and compare categorical data, making it easy to identify patterns and differences between groups. In this section, you'll learn how to create and interpret both frequency and relative frequency bar graphs, while recognizing common mistakes that can make graphs misleading.

Summary

Frequency bar graphDisplays the number of cases in each category.

Relative frequency bar graphDisplays the proportion or percentage of cases in each category.

Bar heightsThe heights of the bars represent the data, while the widths should always remain equal.

Accurate designAccurate bar graphs use a consistent scale and avoid visual distortions such as uneven bar widths or unnecessary 3D effects.

Well-designed bar graphs make categorical data easier to compare, interpret, and communicate.

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 35–38 to reinforce the concepts introduced in the lesson.

Practice what you've learnedComplete the 5 practice questions on pages 39–40. 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 frequency and relative frequency bar graphs from categorical data (e.g., survey responses on commuting methods from a school poll, preference data from a community recreation survey, or product category tallies from a store checkout log).
Building and interpreting bar graphs to compare category sizes (e.g., counts of support requests from a help desk log, student survey data on study locations, or customer feedback categories from a service review form).
Evaluating whether a bar graph clearly represents categorical distributions and deciding whether another display might communicate comparisons more effectively.

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 40) 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.