Math & Statistics · 几何平均与调和平均 · Updated 2026-10-25
What Is Geometric and Harmonic Mean?
Definition
Geometric mean (√n of the product) fits growth rates: +50% then −50% is really −13.4%/yr, not 0%. Harmonic mean (n/Σ(1/xᵢ)) fits rates over a fixed distance, like round-trip speed.
Formula
G = (x₁…xₙ)^(1/n); H = n / Σ(1/xᵢ); always H ≤ G ≤ AM
Worked Example
Returns +20%/−10%/+30%: arithmetic 13.3% but true compound (geometric) rate is 12.0% — a gap that compounds hugely over decades.
Common Misconception
"Average annual return = sum of yearly returns / n" - that is the arithmetic mean; it overstates real compounding for volatile series. "Average speed = (v1+v2)/2" - for equal distances use the harmonic mean: 50 and 40 average to 44.4, not 45.
Matching Calculators
Related Terms
Keep Exploring
Browse the full glossary, or head back to the homepage for 1,435 free online calculators.
Back to glossary