Chapter 3 · Displaying and Summarizing Quantitative Data

Section 3.55-Number Summary, Range and IQR

The five-number summary gives a compact picture of a dataset's distribution — its center, spread, and extremes — in just five values. In this section, you'll learn how to find Q1, Q3, range, and IQR, and how these measures work together to describe variability in data.

Summary

Five-number summaryProvides a quick way to describe a dataset's distribution using the minimum, Q1, median, Q3, and maximum.

Q1 and Q3Q1 and Q3 are the medians of the lower and upper halves of the data, respectively. The median divides the data into those two halves.

Odd vs. even datasetsFor an odd number of values, ignore the median when splitting the data to find Q1 and Q3. For an even number, simply divide the data into two equal halves.

RangeThe difference between the maximum and minimum values — a simple measure of overall spread.

IQRThe interquartile range (Q3 − Q1) measures the spread of the middle 50% of the data and is resistant to outliers.

Range and IQR together describe both the full spread and the typical spread of a dataset — understanding both gives a more complete picture of variability.

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 85–88 to reinforce the concepts introduced in the lesson.

Practice what you've learnedComplete the practice questions on page 89. 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 a five-number summary of employee salary data to describe the distribution of compensation across an organization, identifying where the middle 50% of salaries fall and flagging unusually high or low values (e.g., a human resources analyst preparing an equity review).
Using the IQR to compare variability in test score distributions across two classrooms, determining which group showed more consistent performance and whether the spread differed in meaningful ways (e.g., a curriculum coordinator evaluating the impact of a new instructional approach).
Reporting the range and IQR of daily temperature readings to characterize seasonal climate variability, distinguishing between the full range of extremes and the typical day-to-day variation experienced by most of the population (e.g., an environmental scientist preparing a regional climate summary).

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 89) 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.