Chapter 2 · Displaying and Summarizing Categorical Data

Section 2.5Side-by-Side Bar Graphs

Side-by-side bar graphs help you compare categorical data across groups, making it easier to identify similarities, differences, and possible associations. In this section, you'll learn how to construct and interpret side-by-side bar graphs using contingency tables to communicate comparisons clearly and effectively.

Summary

Contingency tablesOrganize data but may not be the best tool for visual comparison on their own.

Side-by-side bar graphsVisually display frequencies for two categorical variables side by side for easy comparison.

X-axisCategories for one variable go on the x-axis, while the second variable is represented by colored bars.

Subcategory comparisonThis type of graph makes it easier to compare subcategories within a dataset at a glance.

Side-by-side bar graphs turn contingency table data into a visual format that makes group comparisons immediate and intuitive.

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 47–49 to reinforce the concepts introduced in the lesson.

Practice what you've learnedComplete 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.

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:

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

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 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.

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