The word “average” can mean three different things, and choosing the wrong one can be misleading. The mean, median, and mode each answer a slightly different question about your data.
The mean (arithmetic average)
The mean is every value added up and divided by the count. It is what most people mean when they say “average.”
Formula: mean = sum ÷ count
Worked example: The mean of [4, 8, 6, 5, 3] is (4+8+6+5+3) ÷ 5 = 26 ÷ 5 = 5.2. Use the average calculator to verify.
The median
The median is the middle value when the data is sorted. With an odd count, it is the centre value. With an even count, average the two middle values.
Worked example: The median of [3, 4, 5, 6, 8] (sorted) is 5 — the third value in a set of five. For [3, 4, 5, 6, 7, 8], the median is (5+6) ÷ 2 = 5.5.
The mode
The mode is the value that appears most often. A set can have one mode, several modes, or none at all.
Worked example: In [1, 2, 2, 3, 4], the mode is 2. In [1, 1, 2, 2, 3], there are two modes (1 and 2), making it bimodal. In [1, 2, 3, 4, 5], every value appears once, so there is no mode.
When to use which
| Measure | Best when |
|---|---|
| Mean | Data is roughly symmetric with no extreme outliers |
| Median | Data is skewed or has outliers |
| Mode | Data is categorical, or you want the most common case |
In a room of ten people earning £30,000 each, the mean and median are both £30,000. Add one person earning £1,000,000 and the mean jumps to about £118,000 while the median stays at £30,000. The median better represents the typical person. This concept also applies to financial data — see the compound interest guide for how investment returns vary.
Range and spread
Range tells you how spread out the data is: largest value minus the smallest. It is quick to compute but sensitive to a single outlier. For a fuller picture, look at the standard deviation. Use the statistics calculator for these.
Frequently asked questions
When should I use the mean vs the median? Use the mean when the data is roughly symmetric with no extreme outliers. Use the median when the data is skewed or has outliers, because one extreme value can drag the mean far from the centre.
What if there is no mode? If every value appears exactly once, there is no mode. The calculator will report that there is no mode rather than picking an arbitrary value.
Can a data set have more than one mode? Yes. If two or more values tie for the highest frequency, the set is bimodal or multimodal.
What is a weighted mean? A weighted mean gives more importance to some values than others. Multiply each value by its weight, sum those products, then divide by the sum of the weights.