Average Calculator
Calculate arithmetic mean, geometric mean and weighted average.
Which average you use changes the answer
The word "average" covers at least four distinct statistics, and they disagree with each other whenever data is skewed - which is most of the time. Picking the wrong one is how a small number of extreme values ends up misrepresenting an entire dataset.
Formula
arithmetic mean = (x1 + x2 + ... + xn) / n
The weighted mean multiplies each value by its weight before summing, then divides by the total weight rather than the count.
Mean, median, mode, and when each is right
These are not interchangeable. Each answers a different question about the middle of a dataset.
- Mean: the balance point. Uses every value, but a single outlier drags it. Right for symmetric data and for anything where totals matter, such as budgets.
- Median: the middle value when sorted. Ignores how extreme the extremes are. Right for income, house prices, response times - anything with a long tail.
- Mode: the most frequent value. The only average that works on categories, and the only one that can be undefined or have several answers.
- Weighted mean: each value counts in proportion to its importance. Right for grades by credit, prices by volume, or portfolio returns by holding size.
Why median beats mean for income and prices
Take nine people earning 30,000 and one earning 900,000. The mean is 117,000, which describes nobody in the room. The median is 30,000, which describes nine of the ten.
This is why national statistics agencies report median household income and median house prices rather than means. The mean is not wrong - it correctly reports total income divided by headcount - but it answers a question about aggregate, not about the typical case.
A practical heuristic: if the mean sits far above the median, the data has a long right tail, and the median is the more honest summary.
Averaging rates requires a different mean
Driving 60 km at 30 km/h then 60 km at 60 km/h does not average 45 km/h. The trip takes 2 hours plus 1 hour for 120 km, so the true average is 40 km/h.
The correct tool is the harmonic mean, which is n divided by the sum of the reciprocals. Use it whenever the values are rates measured against a fixed numerator - speeds over equal distances, prices per unit, P/E ratios across a portfolio.
For growth rates compounding over time, use the geometric mean instead: multiply the growth factors and take the nth root. Returns of +50% then -50% average to zero arithmetically but produce a real loss of 13.4% a year.
Worked example
Test scores: 45, 52, 58, 61, 63, 67, 71, 74, 78, 96. The mean is 66.5 and the median is 65 - close, because only one value is unusual.
Now replace 96 with 196, a data entry error. The mean jumps to 76.5 while the median stays at 65. The median has told you something the mean has not: nine of the ten values are unchanged.
For a weighted case: modules worth 30, 30, and 60 credits scored 70, 55, and 80. The plain mean is 68.3, but the weighted mean is (70x30 + 55x30 + 80x60) / 120 = 71.25. The larger module pulls the result up, correctly.
Choosing an average
| Data type | Use | Avoid |
|---|---|---|
| Symmetric, no outliers | Arithmetic mean | - |
| Skewed (income, prices) | Median | Mean |
| Categories (colours, brands) | Mode | Mean and median |
| Rates over equal distance | Harmonic mean | Arithmetic mean |
| Growth rates over time | Geometric mean | Arithmetic mean |
| Unequal importance | Weighted mean | Plain mean |
Frequently Asked Questions
Related calculators
References
- NIST/SEMATECH e-Handbook of Statistical Methods
- OECD Glossary of Statistical Terms - mean, median, mode
Last reviewed: 2026-08-07. This page is informational. For legal, medical, tax, or financial decisions, confirm the result with a qualified professional.