Averages: mean, median, mode and range
Three different 'averages' that answer three different questions, plus the range. Which one to use, how to find each, and the outlier that quietly breaks one of them.
"Average" isn't one thing — it's three, and they can give different answers for the same data. Knowing which average a question wants, and why, is half the marks in this topic.
The three averages
Take the data set .
- Mean — add them all up, divide by how many there are. The everyday "average."
- Median — the middle value once they're in order. Here, . (With an even count, take the mean of the middle two.) Always sort the list first.
- Mode — the most common value. Here, appears twice, so the mode is . A set can have more than one mode, or none.
The range — a measure of spread
The range isn't an average at all — it tells you how spread out the data is:
A small range means the values are bunched together; a large one means they're scattered.
Which average to use
| Average | Best when… | Weakness |
|---|---|---|
| Mean | Data is evenly spread | Dragged badly by outliers |
| Median | There's an extreme value | Ignores most of the data |
| Mode | Data is categories (shoe size, colour) | May not exist or be central |
The mean's weakness matters. Add one millionaire to a room and the mean wealth soars, even though almost everyone is unchanged — the median is the honest "typical" value there, because one huge outlier can't drag it.
Sort the data before you touch the median or mode. The single most common error is reading the middle of an unsorted list. Put the numbers in order first, every time.
Last revised 22 April 2025.