How to Calculate Geometric Mean

What is Geometric Mean?

The geometric mean is the nth root of the product of n numbers. It's used for rates of change, growth rates, and situations where multiplicative processes occur.

Formula

GM = ⁿ√(x₁ × x₂ × ... × xₙ)

Step-by-Step Guide

1Multiply all n numbers together
2Take the nth root of the product
3Use logarithms to avoid overflow with large numbers

Worked Examples

Input

Numbers: 2, 8, 4

Result

GM = 4

∛(2×8×4) = ∛64 = 4

Common Mistakes to Avoid

✕Using arithmetic mean instead
✕Root degree not matching number of values

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