Chapter 2 · Displaying and Summarizing Categorical Data

Section 2.1Frequency and Relative Frequency Tables

Raw data can be difficult to interpret until it is organized. In this section, you'll learn how frequency and relative frequency tables organize categorical data, making it easier to identify patterns, compare groups, and communicate information effectively.

Summary

Frequency tableDisplays counts of occurrences for different categories.

Relative frequencyShows counts as fractions, decimals, or percentages. Found by dividing a category's count by the total count.

Sum checkThe sum of all relative frequencies should always equal 1 (or 100%).

Organizing raw data into frequency and relative frequency tables is the first step toward identifying patterns and communicating findings clearly.

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 26–28 to reinforce the concepts introduced in the lesson.

Practice what you've learnedComplete the 3 multi-part practice questions on pages 28–29. 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:

Organizing raw categorical responses (e.g., survey answers, preferences, or selections) into frequency and relative frequency tables to reveal distribution patterns.
Summarizing 100+ individual categorical responses into structured comparative views that support interpretation and decision-making.
Using aggregated categorical data to write a brief evidence-based recommendation or summary for a real-world stakeholder (e.g., school, business, or program leader).

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 29) 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.