Definition · Plain-language
Mean, median and mode
Mean, median and mode are the three measures of central tendency that summarise a dataset with a single typical value; the range adds a simple measure of spread.
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The three measures of central tendency
The mean is the arithmetic average: add every value and divide by the number of values. The median is the middle value once the data are sorted in order — or the average of the two middle values when there is an even count. The mode is the value that occurs most often, and a dataset can have one mode, several, or none at all. Each gives a single "typical" figure, but they answer slightly different questions, so the right choice depends on the data and the purpose.
When to use each
The mean uses every value and is ideal for roughly symmetric data, but it is sensitive to outliers and skew — a single extreme value can drag it away from the bulk of the data. The median is robust to outliers and is preferred for skewed distributions such as incomes or house prices, where a few large values would distort the mean. The mode is the only measure usable with categorical (nominal) data, such as the most common blood type, and is useful for spotting the most typical category.
The range and why spread matters
A measure of central tendency on its own can mislead: two datasets can share the same mean yet differ wildly in how spread out they are. The range — the largest value minus the smallest — is the simplest measure of dispersion and gives a quick sense of how far the data stretch. It is easy to compute but very sensitive to outliers, since it depends only on the two extreme values. For a fuller picture of spread, analysts turn to the interquartile range, variance and standard deviation.
Key facts
At a glance
- Mean: the arithmetic average (sum of values ÷ number of values)
- Median: the middle value when the data are ordered
- Mode: the most frequently occurring value (can be none or several)
- Range: largest value minus smallest value (a measure of spread)
- Robustness: the median resists outliers; the mean does not
- Categorical: only the mode works with nominal categories
Common misconceptions
What people often get wrong
Often heard: The "average" always means the mean.
Actually: In everyday use "average" usually means the mean, but in statistics it is a general term for any measure of central tendency — the median and mode are averages too. The correct choice depends on the data’s shape.
Often heard: The mean is always the best summary of a typical value.
Actually: Not for skewed data or data with outliers. A few extreme values can pull the mean away from most of the data, where the median gives a more representative centre — which is why incomes are usually reported as medians.
Often heard: Every dataset has exactly one mode.
Actually: No. A dataset can be unimodal, bimodal or multimodal, or have no mode at all if every value occurs equally often. The mode is the only one of the three measures that can be undefined or non-unique.
Going deeper
