Mean, Median and Mode Explained
Mean, median and mode are three ways of describing the “typical” value in a set of numbers. They often disagree — and the disagreement itself tells you something about the data.
One data set, three averages
Consider the prices of seven houses on a street (in thousands): 210, 225, 230, 230, 245, 260, 890.
| Measure | How to find it | Result |
|---|---|---|
| Mean | add all values, divide by the count: 2,290 ÷ 7 | ≈ 327.1 |
| Median | middle value when sorted (the 4th of 7) | 230 |
| Mode | most frequent value | 230 |
One mansion pulls the mean far above what six of the seven houses cost. The median and mode describe a typical house much better.
The mean
The arithmetic mean uses every value, which is its strength and its weakness. It is ideal for roughly symmetric data without extreme values — test scores in a class, daily temperatures, repeated measurements. It is also the only one of the three that lets you recover the total: mean × count = sum.
The median
The median is the middle of the sorted data (or the mean of the two middle values when there is an even count). Half the values lie below it, half above. Because it ignores how far the extremes are, it is the standard average for skewed data such as incomes, house prices and waiting times.
The mode
The mode is the most common value. It is the only average that works for categories (the most popular color or shoe size), and it can reveal clusters: a data set with two modes may be mixing two groups. Data sets can have no mode, one mode or several.
Skew in one sentence
When the mean is well above the median, the data has a long tail of high values (right skew); when it is well below, a long tail of low values (left skew). When they are close, the data is roughly symmetric.
Choosing an average
- Symmetric numeric data, no outliers → mean.
- Skewed data or outliers → median.
- Categories, or “most common” → mode.
- Values of different importance → weighted mean.
- Always report the spread too (range or standard deviation) — an average alone hides how varied the data is.