Chapter 2: Displaying and Summarizing Categorical Data

• Contingency tables organize data but may not be the best for visual comparison.
• Side-by-side bar graphs visually display frequencies for two categorical variables.
• Categories for one variable go on the x-axis, while the second variable is represented by colored bars.
• This type of graph makes it easier to compare subcategories within a dataset.

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

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

Step 1: Watch the lesson video

Watch the lesson video and take notes on the key ideas.

Step 2: Read the section

Read pages 47-49 to reinforce the concepts introduced in the lesson.

Step 3: Practice what you've learned

Complete the 4 practice questions on pages 50-51. Check your work using the Answer Key, then review and correct any questions you missed before moving on.

Step 4: Think like a statistician
Explore Enrichment: Role-Based Statistical Analysis Tasks and the Chapter Dataset to apply statistical thinking in real-world contexts.

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

Examples of authentic statistical work supported by this section include:

• comparing outcomes across two groups by constructing side-by-side bar graphs from contingency table data (e.g., internet access and online learning participation from a school technology survey, or housing stability and employment status from a community study) 
• communicating differences between populations using visual comparisons and supporting percentages (e.g., employee satisfaction by work arrangement from a workplace survey, or vaccination status by age group from a public health report) 
• evaluating whether two categorical variables appear to be associated by interpreting side-by-side bar graphs and contingency tables (e.g., transportation choice by neighborhood from a commuter survey, or product preference by age group from market research)

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

Enrichment: Role-Based Statistical Analysis 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 51) 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.