Statistics for Researchers › Module 1: Thinking with data
Mean, median and outliers
Lesson 2 of 3 · 2 min
The mean is the average: add everything up and divide by how many. The median is the middle value when you sort the data. They answer slightly different questions, and they can tell very different stories.
When they differ
ExampleTen people in a room earn ₹30,000 a month each. One more person walks in who earns ₹30 lakh a month. The mean income jumps to about ₹3 lakh. The median is still ₹30,000. Which number describes "a typical person in the room"? The median.
The mean is pulled by outliers: values far from the rest. The median is not.
Which to use
| Data | Better summary |
|---|---|
| Roughly symmetric, no big outliers | Mean |
| Skewed (income, house prices, reaction times) | Median |
| You care about the total (total cost, total energy) | Mean |
- Roughly symmetric, no big outliers
- Better summary: Mean
- Skewed (income, house prices, reaction times)
- Better summary: Median
- You care about the total (total cost, total energy)
- Better summary: Mean
Many papers report both. If they are far apart, the data is skewed, and you should know that.
Outliers: look, don't just delete
An outlier can be a mistake (a typing error, a broken sensor) or a real, important case. Never delete outliers just because they are inconvenient. Check where they came from, decide on a rule before looking at the results, and report what you removed and why.
RememberMean for symmetric data, median for skewed data. Investigate outliers; never quietly delete them.