stats

Geometric Mean

GM via log-sum, weighted GM, comparison with AM and HM — number line showing all three means with context panel.

Mode

Input

Values (all must be positive)

Results

Count n—

Geometric Mean GM—

Arithmetic Mean AM—

Harmonic Mean HM—

GM as % of AM—

HM ≤ GM ≤ AM—

GM = exp(Σln(xᵢ)/n) · log-sum avoids overflow

When to use each mean

GMgrowth rates, investment returns, ratios, multiplicative processes

AMadditive quantities, temperatures, lengths, scores

HMaverage speeds, rates, P/E ratios, parallel resistances