Lesson 2: When the Average Lies

About 30 minutes — Discussion-based lesson

What You Will Learn

This lesson covers:

How one extreme value changes the mean dramatically
The billionaire in the room: why average income is misleading
When the mean does not represent most people
Introduction to median: the middle value

How one extreme value changes the mean dramatically

This section covers the key ideas about how one extreme value changes the mean dramatically. Discuss with your group or family and explore the concepts together.

The billionaire in the room: why average income is misleading

This section covers the key ideas about the billionaire in the room: why average income is misleading. Discuss with your group or family and explore the concepts together.

When the mean does not represent most people

This section covers the key ideas about when the mean does not represent most people. Discuss with your group or family and explore the concepts together.

Introduction to median: the middle value

This section covers the key ideas about introduction to median: the middle value. Discuss with your group or family and explore the concepts together.

Check Your Understanding

1. How can one outlier change the mean?

Answer: If 9 people earn $40,000 and 1 person earns $1,000,000, the mean income is $136,000 — but nobody actually earns that amount. The one extreme value pulled the mean way up.

2. What is the median?

Answer: The median is the middle value when all numbers are in order. It is less affected by outliers than the mean. In the income example, the median would be $40,000 — much more representative.

3. When is the mean misleading?

Answer: When the data has extreme outliers, when the data is very spread out, or when the data is not symmetric. In these cases, the median often tells a better story.

4. Should you always use the mean?

Answer: No! The mean is one tool among several. Sometimes the median is better. Always think about whether the mean actually represents the typical case.

Key Takeaways

How one extreme value changes the mean dramatically
The billionaire in the room: why average income is misleading
When the mean does not represent most people
Introduction to median: the middle value

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