Mean, median, and outliers
The following invented classroom dataset records reading minutes for ten learners on one evening: 10, 15, 15, 20, 20, 20, 25, 25, 30, 60. It is practice data, not research about children.
What is the mean with all ten values?
📝 Investigate the unusual value
Remove 60 temporarily. The other nine total 180, so their mean is 20. Explain why removing a large value changes the mean more than the median. Do not delete unusual observations from real work merely because they are inconvenient: check whether the measurement is valid.
📝 Make a claim
Write two sentences answering: Which single measure would you use to describe a typical evening in this small dataset? Cite your calculation and explain its limitation. A reasonable answer chooses the median because the 60-minute value pulls the mean upward. This sample cannot tell us what all learners do.
✅ Check your understanding
Which measure uses only the minimum and maximum?
Can these invented ten observations establish a national average?
✏️ Try a second supplied dataset
A second invented group records 10, 15, 15, 20, 20, 20, 25, 25, 30, 30 minutes. Calculate mean, median, and range before checking the answer below. Which changed from the first group, and why?
🔑 Worked answer
Total 210; mean 21; median 20; range 20 minutes. Replacing 60 with 30 lowers the mean from 24 to 21 and range from 50 to 20. The middle pair remains 20, so the median is unchanged.