Chapter 3 · Displaying and Summarizing Quantitative Data

Section 3.7Introduction to Outliers

Outliers are data points that stand apart from the rest — and deciding what to do with them is one of the most important judgment calls in statistical analysis. In this section, you'll learn what makes a value an outlier, how outliers affect the mean and median differently, and why investigating them matters.

Summary

OutlierA data point that significantly differs from the rest of the dataset — either unusually high or unusually low relative to the other values.

Effect on the meanOutliers can distort the mean substantially, pulling it toward the extreme value and making it a poor representation of the typical case.

Effect on the medianThe median is resistant to outliers — a single extreme value has little or no effect on the middle of an ordered dataset.

Investigating outliersDetermining whether an outlier is a data entry error, a measurement mistake, or a genuinely unusual but valid observation is crucial before deciding how to handle it.

Outliers are not automatically errors — they can be the most important data points in a dataset. Investigating them carefully is a hallmark of rigorous statistical practice.

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 96–99 to reinforce the concepts introduced in the lesson.

Practice what you've learnedComplete the practice questions on page 99. 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:

Identifying an unusually high hospital readmission rate for one facility in a statewide dataset, then investigating whether it reflects a genuine quality-of-care issue, a data reporting error, or a difference in patient population — and deciding whether to include or flag it in the final analysis (e.g., a health policy researcher preparing a hospital performance report).
Detecting an outlier in a dataset of product defect rates across manufacturing plants, comparing the mean with and without the outlier to quantify its influence, and reporting both values with appropriate context so decision-makers understand the full picture (e.g., a quality assurance analyst conducting a production audit).
Examining an extreme value in a dataset of student test scores — determining whether it represents a student who was absent for part of the test, a scoring error, or a genuinely exceptional performance — and justifying the decision to retain or exclude it in the summary statistics (e.g., a data analyst supporting an academic research study).

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 99) 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.