Chapter 3 · Displaying and Summarizing Quantitative Data

Section 3.4Understanding and Finding the Median

The median is a powerful measure of center that resists the pull of extreme values, making it especially useful when data is skewed or contains outliers. In this section, you'll learn how to find the median from lists, frequency tables, and histograms — and when to choose it over the mean.

Summary

MedianThe middle value in an ordered dataset. If there is an even number of values, the median is the average of the two middle numbers.

Frequency tablesThe median is found by identifying the category that contains the middle value based on cumulative frequencies.

HistogramsCreate a frequency table from the histogram first, then use it to determine where the median lies.

Median vs. meanThe median is more reliable than the mean when dealing with skewed data or outliers, since it is not affected by extreme values.

Choosing the median over the mean is a judgment call rooted in the shape of the data — understanding when each measure is appropriate is a core statistical skill.

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 80–83 to reinforce the concepts introduced in the lesson.

Practice what you've learnedComplete the practice questions on pages 83–84. 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:

Reporting median household income rather than mean income to describe a neighborhood's economic profile, recognizing that a small number of very high earners would distort the mean upward (e.g., a policy analyst preparing a community needs assessment).
Locating the median from a frequency table of patient wait times to identify the typical experience for most patients, rather than the average inflated by a few unusually long waits (e.g., a hospital operations analyst evaluating emergency department efficiency).
Comparing median home sale prices across neighborhoods over time to track market trends, using the median to avoid distortion from a small number of luxury sales (e.g., a real estate researcher preparing a regional market report).

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 84) 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.