When the average moves

Can the average change while the typical middle value stays put?

Move one observation. Watch both summaries.

Largest observation 9

Mean 6.29

Median 6

Values · 4, 5, 5, 6, 7, 8, 9

Check the explanation

Seven illustrative observations, with the largest constrained to 9–45. These are example values, not measurements from a study.

Teaching notes · 20 minutes

Students should be able to…

Calculate the mean and median, and explain their different responses to an extreme observation.

Before this lesson

Adding numbers, dividing by the number of observations, and ordering a list.

Ask first

Seven observations are 4, 5, 5, 6, 7, 8 and 9. Predict what happens to the mean and median if only the last observation becomes 40.

A misconception to listen for

The median is not always fixed when one value changes. It is fixed here because the adjusted value stays at the upper end of the ordered list.

Student task

Choose a value that makes the mean equal to 10. Explain why the median remains 6 for every value allowed by this demonstration.

Exit question & expected reasoning

Why does increasing the largest observation change the mean but leave the median at 6?

Every observation contributes to the sum used for the mean. The fourth ordered observation is still 6, so the median of these seven values is unchanged.

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