What pulls the average?
Five numbers sit on a beam. The mean is where it balances, so dragging one number out to the end tips the whole thing. The median is only ever the middle one, and it hardly notices.
mean7.4 median8
All five are close together, so the two agree.
- The five values
- 4, 6, 8, 8, 11
- Range
- 7
Drag the orange dot along the beam.
Where is the odd one out?
Ready to try some? Mean, median and mode worksheets
Where it usually goes wrong
“Average” is heard as one thing. The mean is a balance point and one far-off value drags it; the median is a position and hardly notices. Quoting the mean salary in a room containing one billionaire is not a lie about the arithmetic, it is the wrong average for the question.
Try this
- Press In the pack and read the two numbers. With five values close together the mean and the median agree, which is why the difference is so easy to miss.
- Now press Far out. The mean chases the value you dragged; the median stays on the middle one.
- Drag the odd value further and further. There is no limit to how far the mean will follow it.
Where this goes next
Every statistic in a news report is one of these two, chosen by somebody, and knowing which was chosen is most of reading the report.