Chapter 4 · Box and Whisker Plots

Section 4.1Box and Whisker Plots with No Outliers

A box and whisker plot turns the five-number summary into a visual story about a dataset's distribution — showing the center, spread, and shape at a glance. In this section, you'll learn to construct and interpret box plots for datasets with no outliers, and use them to describe skewness and variability.

Summary

Five-number summaryThe foundation of a box plot: minimum, Q1, median, Q3, and maximum. The box spans from Q1 to Q3, and the whiskers extend to the minimum and maximum values.

IQR and the boxThe box represents the middle 50% of the data (the interquartile range). Its width reflects how spread out the central portion of the data is.

WhiskersEach whisker covers 25% of the data — the lower whisker from the minimum to Q1, and the upper whisker from Q3 to the maximum.

SkewnessThe position of the median within the box reveals skewness: a median closer to Q1 suggests right skew, while a median closer to Q3 suggests left skew.

SpreadBoth the IQR (box width) and the range (total whisker span) help assess how spread out the data is across the distribution.

Box plots are especially powerful for comparing distributions side by side — a skill developed further in Section 4.4.

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 119–123 to reinforce the concepts introduced in the lesson.

Practice what you've learnedComplete the practice questions on page 123. 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 box plot of annual rainfall data across a region to visualize the distribution of precipitation, identify the typical range, and assess whether the data is symmetric or skewed (e.g., a climate scientist preparing a regional weather summary).
Using a box plot to display the distribution of student exam scores, identifying the median performance and the spread of the middle 50% of students to inform instructional decisions (e.g., a teacher analyzing class performance data before a parent-teacher conference).
Interpreting a box plot of delivery times to assess consistency and identify whether the distribution is right-skewed, indicating that most deliveries are fast but a few take significantly longer (e.g., a logistics analyst evaluating supply chain performance).

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 123) 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.