"The average" is not one thing. There are three common measures of central tendency — mean, median, and mode — and they can tell very different stories about the same data. Knowing which to use is one of the most practical skills in statistics.
The three measures
- Mean — add up all values and divide by how many there are. The everyday "average."
- Median — sort the values and take the middle one (or the average of the two middle ones). Half the data is below it, half above.
- Mode — the value that appears most often. A dataset can have one mode, several, or none.
Worked example. Salaries (in thousands): 30, 32, 35, 38, 40, 250.
Mean = 70.8 · Median = 36.5 · Mode = none.
The mean (70.8) suggests a typical salary far above what anyone except one person earns. The median (36.5) describes the group far more honestly. That one big value — an outlier — is the whole story.
The key difference: sensitivity to outliers
The mean uses every value, so a single extreme number drags it up or down. The median only cares about position, so it barely moves. This is why:
| Situation | Best measure | Why |
|---|---|---|
| Symmetric data, no outliers | Mean | Uses all information, most efficient |
| Skewed data or outliers (income, house prices) | Median | Not distorted by extremes |
| Categorical data (favourite colour, size) | Mode | Only measure that works on non-numbers |
How skew shifts the mean
In a perfectly symmetric distribution, mean = median = mode. When data is right-skewed (a long tail of high values, like income), the mean is pulled above the median. When left-skewed, the mean falls below the median. Comparing the mean and median is itself a quick check for skew — if they're far apart, your data isn't symmetric.
Which should you report?
- Reporting a "typical" value for skewed money data (salaries, prices, donations)? Use the median.
- Doing further statistics like a t-test or confidence interval? Those are built on the mean.
- Describing the most common category or size? Use the mode.
Often the honest answer is to report more than one, plus a measure of spread like the standard deviation.
Calculate all three at once
Descriptive Statistics Calculator →Paste your data to get mean, median, mode, standard deviation, quartiles, skewness, and more.Related reading: Confidence intervals explained · Effect size explained · Choosing a statistical test.