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Mean, median and outlier practice
The mean uses every numerical value, while the median locates the middle after sorting. An extreme observation can move the mean substantially without moving the median as much.
By ExamCat · Original study lesson · Published September 24, 2026
Understand the method
Calculate the mean by dividing the sum by the count. For an even count, the median is the average of the two middle sorted values. Neither statistic alone describes the full distribution, so inspect spread and unusual values too.
Worked example, step by step
Compare the mean and median for 2, 3, 4, 5 and 21.
- The sum is 35 and the count is five, so the mean is 7.
- The sorted middle value is 4, so the median is 4.
- The high observation 21 pulls the mean above most of the data.
- Removing 21 gives a different dataset with mean 3.5 and median 3.5, but an unusual value should not be removed merely because it is inconvenient.
A mistake to watch for
“Average” can be ambiguous. Name the statistic and state whether you changed the dataset. An extreme value might be valid evidence rather than a recording error.
Try it yourself: three questions
Write an answer before opening the explanation. For calculations, keep your units and intermediate steps; for concepts, state the reason for your choice.
1. Find the median of 8, 1, 6 and 3.
Show answer and explanation
Sort to 1, 3, 6, 8. The median is (3 + 6)/2 = 4.5.
2. Every observation increases by 10. What happens to mean and median?
Show answer and explanation
Both increase by 10. The entire distribution shifts without changing the relative ordering.
3. Can two datasets have the same mean but different spread?
Show answer and explanation
Yes. For example, 4, 5, 6 and 0, 5, 10 both average 5, but the second set is more spread out.
Build your next practice session
Mark the first step where your reasoning differed from the explanation. Turn that step into a question, answer it without looking, then change one condition in the example and explain what would change. A correct guess is a reason to revisit the method.
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