Chapter 3 · Displaying and Summarizing Quantitative Data

Section 3.6Understanding and Finding the Mean

The mean is the most widely used measure of center, but calculating it correctly — especially from grouped data — requires understanding how values and their frequencies interact. In this section, you'll learn how to find the mean from a list, a frequency table, and a histogram, and when the mean is the right measure to use.

Summary

Mean (from a list)The sum of all values divided by the number of values — calculated directly when individual data points are available.

Mean (from a frequency table)Estimated using midpoints weighted by their frequencies. The formula Mean = Σ(x · f) / Σf allows us to calculate the mean from grouped data.

Mean (from a histogram)Extract a frequency table from the histogram first, then apply the same weighted midpoint process used for frequency tables.

When to use the meanThe mean is most appropriate for symmetric distributions without extreme outliers, where all values contribute meaningfully to the center.

The mean is sensitive to every value in the dataset — which makes it powerful for symmetric data and potentially misleading when the distribution is skewed or contains outliers.

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 90–94 to reinforce the concepts introduced in the lesson.

Practice what you've learnedComplete the practice questions on pages 94–95. 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:

Estimating the mean commute time from a frequency table of grouped travel data, using weighted midpoints to approximate the average when individual times are not available (e.g., a transportation planner analyzing regional commuting patterns from survey data).
Calculating the mean score on a standardized assessment from a histogram of student results, then comparing it to the median to determine whether the distribution is symmetric or skewed and which measure better represents typical performance (e.g., an assessment coordinator reviewing district-wide test results).
Computing the mean daily energy consumption from a frequency table of household usage data to estimate total demand and inform infrastructure planning, recognizing that the weighted mean accounts for how many households fall in each usage range (e.g., a utility analyst preparing a load forecasting 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 95) 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.