Median vs. Mean
“Median” and “mean” are different measures of central tendency. The median depends on the ordered middle position, while the arithmetic mean uses the sum of all observations divided by their count.
In statistics, the “median” is the middle value after the values are ordered; the arithmetic “mean” is found by adding the values and dividing by how many values there are.
Key details
Choose the right form
| Meaning / situation | Form / construction | Decision |
|---|---|---|
| middle value after observations are ordered | median | Use the middle-position measure. |
| arithmetic average | mean | Add the values and divide by the number of values. |
Quick tests
Meaning / construction test
Do you need the middle ordered value rather than the arithmetic average?
If yes: Use “median.”
If no: Use “mean” if you are calculating the arithmetic average.
Caveat: This guide distinguishes the arithmetic mean from the median; other kinds of mean exist in mathematics and statistics.
Examples
For 2, 4, and 100, the median is 4.
The ordered middle value is 4.
For 2, 4, and 100, the mean is about 35.3.
The arithmetic average is the sum divided by three.
Report which measure you use rather than calling both “average” without clarification.
The labels identify different statistical summaries.
Further guidance
Core difference
“Median” means the ordered middle; arithmetic “mean” means total divided by count.
Fast Test
Order the values to find the median. Add all values and divide by the number of values to find the arithmetic mean.
Usage Boundary
The two measures can be equal in some data sets, but that does not make the terms interchangeable because they are calculated differently.
Sources and evidence
Sources are shown with the role they play in this guide. Historical or style-sensitive claims are kept within the evidence boundary described above.
- Median — Cambridge Dictionary (opens in a new tab)Cambridge University Press · Direct mathematical definition of median as the middle value in an ordered series.
- Mean — Cambridge Dictionary (opens in a new tab)Cambridge University Press · Direct mathematical definition of arithmetic mean as total divided by number of values.