Data: centre, spread and outliers
Choose a summary that fits the shape and context of the data.
Before you begin
- Ordering numbers
- Arithmetic mean
Compare the mean and median
The mean uses every numerical value: add the values and divide by their count. The median is the middle value after ordering; for an even count, average the two middle values. A large outlier can pull the mean towards it while leaving the median almost unchanged. Neither measure is always best: explain which aspect of the data matters in context.
Report variability as well as centre
Two groups can have the same centre but different spread. The range is maximum minus minimum and uses only the two extremes. Always include units and consider sample size and selection. A summary of five observed journeys does not automatically describe all journeys or prove why one was slower.
Worked example
For journey times 8, 9, 10, 11 and 32 minutes, find the mean and median.
Show the worked solution
- Add the times: 8 + 9 + 10 + 11 + 32 = 70.
- Divide by 5 to obtain a mean of 14 minutes.
- The ordered middle value is 10; the unusually long trip raises the mean.
Mean 14 minutes; median 10 minutes.
Try it yourself
What is the median of 3, 5, 7 and 21?
Common mistakes
- Sort the data before locating the median.
What can you explain now?
For 4, 4, 6, 6, 30, find the median and range. Explain whether the mean describes a typical value well.
Compare with the explanation
Median 6; range 26. The mean of 10 is pulled upward by 30.
The middle ordered value is 6. Subtract 4 from 30 for the range. Most observations are 4 or 6, so the median better represents their typical size in this sample.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗