Mean
Find the arithmetic, weighted, geometric and harmonic mean of numbers with a step-by-step solution. Exact answer in fractions.
The mean calculator finds the arithmetic, weighted, geometric and harmonic means of a set of numbers. Numbers can be whole, decimal or fractions — the answer is exact, for example 7/3. For positive numbers the calculator compares all kinds of means.
Mean formulas
| Mean | Formula | Used for |
|---|---|---|
| Arithmetic | x̄ = (x1 + x2 + … + xn) / n | average grade, average temperature |
| Weighted | x̄w = Σxiwi / Σwi | average price, weighted grades |
| Geometric | G = ⁿ√(x1 · x2 · … · xn) | average growth rate |
| Harmonic | H = n / (1/x1 + … + 1/xn) | average speed over equal distances |
Example 1. Grades 4, 7, 9, 5, 10: x̄ = 35 / 5 = 7.
Example 2. 10 kg at $5, 6 kg at $4, 4 kg at $3: average price (50 + 24 + 12) / 20 = $4.3.
Example 3. Half the way at 60 km/h and half at 40 km/h. The average speed is the harmonic mean: 2 / (1/60 + 1/40) = 48 km/h, not 50.
For positive numbers always H ≤ G ≤ x̄; all means are equal only when all numbers are the same.
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