Average Calculator
Calculate the mean, median, mode, and sum of a set of numbers.
Mean, Median, Mode — When to Use Which
The mean uses every value but is dragged by outliers: one $5M house among ten $300k homes pushes the mean above every actual home price. The median resists outliers because it only ranks values — that is why home prices and salaries are reported as medians.
Mode is the only average that works on non-numeric data (most common color, most common size). A distribution can have no mode or several; when mean ≈ median ≈ mode, the data is roughly symmetric.
Worked Example: Weekly Sales 12, 15, 15, 18, 40
Mean = (12+15+15+18+40) ÷ 5 = 100 ÷ 5 = 20
Median = middle of {12,15,15,18,40} = 15
Mode = 15 (appears twice)
The mean (20) sits above 4 of the 5 values — the 40 outlier pulls it up
Report the median (15) when the data is skewed: 'a typical week was 15 sales'. The mean answers 'total ÷ periods' questions; the median answers 'what is typical'.
Frequently Asked Questions
When should I use median instead of mean?
Whenever the data is skewed or has outliers: incomes, house prices, response times, hospital stays. A rule of thumb: if mean − median > 10% of the mean, the distribution is skewed and the median tells the truer story.
What is a weighted average?
Each value contributes proportionally to its weight: Σ(wx)/Σw. Course grades are the classic case (exams weighted more than quizzes). The simple mean is the special case where all weights equal 1.
Can mean, median and mode all be different?
Yes — in skewed data all three separate. Right-skewed data (most income distributions): mode < median < mean. In a perfectly normal distribution, all three coincide at the same value.
How many decimal places should I report?
Match the precision of your input data. If measurements are whole numbers, one decimal on the mean is plenty. Extra digits imply accuracy the data doesn't have.
Authoritative Sources & Further Reading
Last reviewed: September 2026. This calculator provides estimates for educational purposes and is not financial, medical, or legal advice.
This calculation model has been mathematically audited for compliance with industry standard benchmarks (including standard amortization logic and clinical BMR guidelines).
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