Mean, Median & Mode Calculator
Find the mean (average), median (middle), and mode (most frequent) of any data set. Also calculates range, sum, minimum and maximum.
| Country | Official Measure | Agency | Why Median? |
|---|---|---|---|
| 🇺🇸 United States | Median household income | US Census Bureau | Right-skewed income distribution |
| 🇬🇧 United Kingdom | Median weekly earnings | ONS (Office for National Statistics) | Avoids billionaire distortion |
| 🇦🇺 Australia | Median weekly income | ABS (Australian Bureau of Statistics) | Better represents typical worker |
| 🇨🇦 Canada | Median total income | Statistics Canada | Standard for economic reporting |
| 🇩🇪 Germany | Median Äquivalenzeinkommen | Destatis (Federal Statistical Office) | EU-standard methodology (SILC) |
| 🇯🇵 Japan | Median household income | Ministry of Health Labour | Income inequity measurement |
Frequently Asked Questions
Can a data set have no mode or multiple modes?
Yes. No mode: all values appear exactly once — e.g., 1, 2, 3, 4, 5. One mode (unimodal): one value is most frequent — e.g., 1, 2, 2, 3, 4. Two modes (bimodal): two values tied — e.g., 1, 2, 2, 3, 3. Multiple modes (multimodal): more than two values tied. In UK A-Level and GCSE maths, students learn that "no mode" is a valid answer. In US K-12, the mode is often discussed in the context of grouped frequency distributions where it always exists.
When is the mean a misleading average?
The mean is misleading when data is heavily skewed — particularly with outliers. Classic examples: Bill Gates walks into a bar, and the average net worth of everyone in the bar becomes $1 billion (median barely changes). Class test scores: if one student scores 100 and everyone else scores 40, the mean (48) doesn't represent any student well. House prices: London mean is pulled up by multi-million pound properties; the median better reflects what a typical buyer pays. In these cases, the median is a better measure of central tendency.