Mean vs Median: Which Should You Use?
The mean and median both describe the centre of a data set — but they can give very different answers. Choosing the right one depends on the shape of your data and what you want to communicate.
At a Glance
| Mean | Median | |
|---|---|---|
| Definition | Sum ÷ count | Middle value (sorted) |
| Formula | x̄ = Σx / n | Middle of sorted list |
| Affected by outliers | Yes — strongly | No — robust |
| Best for | Symmetric data | Skewed data or outliers |
| Symbol | x̄ (sample) or μ (pop.) | Md or M |
How Outliers Change Everything
Seven people earn (k€/yr): 28, 30, 31, 32, 33, 35, 200
- Mean = (28+30+31+32+33+35+200) / 7 = 389 / 7 ≈ 55.6 k€
- Median = 4th value = 32 k€
The mean is inflated by the single high earner and does not represent anyone in the group. The median of 32 k€ accurately reflects what a typical person earns. This is exactly why official income statistics use the median.
Skewed Distributions
When data is right-skewed (long tail on the right — like income, house prices, or waiting times), the mean is higher than the median because the few large values pull the mean up.
When data is left-skewed (long tail on the left — like age at retirement), the mean is lower than the median.
Quick rule:
mean > median → right-skewed
mean < median → left-skewed
mean ≈ median → roughly symmetric
Which One to Report?
Use the mean when:
- Data is symmetric with no extreme outliers (exam scores, daily temperatures, product weights)
- You need to compute further statistics — std dev, confidence intervals, regression
- Every value genuinely belongs and should count equally
Use the median when:
- Data is skewed or contains outliers (income, house prices, response times)
- You want to describe the "typical" individual (50% above, 50% below)
- Outliers exist but are real, not errors
Best practice: report both when in doubt — the gap between them reveals the skewness of the distribution. The statistics calculator shows you both at once.