How to Calculate Geometric Mean
What is Geometric Mean?
The geometric mean is the nth root of the product of n numbers. It is the correct average for quantities that multiply (growth rates, investment returns) rather than add.
Step-by-Step Guide
- 1GM = (x₁ × x₂ × ... × xₙ)^(1/n)
- 2Always ≤ arithmetic mean
- 3For investment returns: GM = (final/initial)^(1/n) − 1
Worked Examples
Input
Annual returns: +50%, −50%, +50%
Result
GM = (1.5×0.5×1.5)^(1/3)−1 = −6.1%/yr
AM would give +16.7% — completely misleading
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