Chapter 4 · Box and Whisker Plots

Section 4.2Box and Whisker Plots with Outliers

Not all data points belong inside the whiskers. In this section, you'll learn how to use the 1.5 × IQR Rule to identify outliers, mark them separately on a box plot, and adjust the whiskers so the visual accurately represents the bulk of the data — without letting extreme values distort the picture.

Summary

1.5 × IQR RuleA value is an outlier if it falls more than 1.5 times the IQR below Q1 or above Q3. This rule provides a consistent, objective method for identifying unusual values.

Lower FenceCalculated as Q1 − 1.5 × IQR. Any data value below this threshold is flagged as a lower outlier.

Upper FenceCalculated as Q3 + 1.5 × IQR. Any data value above this threshold is flagged as an upper outlier.

Adjusted whiskersWhen outliers are present, the whiskers extend only to the highest and lowest values within the acceptable range — not to the absolute minimum and maximum.

Outlier markersOutliers are plotted as individual points (typically dots or asterisks) beyond the whiskers, making them visually distinct from the rest of the distribution.

Identifying and displaying outliers correctly prevents misleading visual representations and draws attention to values that may warrant further investigation.

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 124–127 to reinforce the concepts introduced in the videos.

Practice what you've learnedComplete the practice questions on page 128. 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:

Applying the 1.5 × IQR Rule to a dataset of household incomes to identify extreme high earners as outliers, then constructing an adjusted box plot that accurately represents the income distribution for the majority of households (e.g., an economist preparing a regional income inequality report).
Detecting outliers in a dataset of patient recovery times after surgery, flagging unusually long recoveries for further clinical review, and displaying the adjusted distribution to communicate typical outcomes to hospital administrators (e.g., a healthcare analyst evaluating post-operative care quality).
Identifying outlier values in a dataset of product defect rates across manufacturing facilities, investigating whether the extreme values reflect genuine quality issues or data entry errors, and presenting findings in a quality control report (e.g., a process engineer conducting a manufacturing audit).

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 128) 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.