Calculate the geometric mean of positive numbers, ideal for growth rates and ratios.
The geometric mean is the nth root of the product of n values. It represents the central tendency of multiplicative data such as growth rates, investment returns, and ratios. It is computed via logarithms to avoid overflow.
Geometric Mean
G = (x₁ × x₂ × ... × xₙ)^(1/n) = exp(mean(ln(values)))
Use geometric mean for multiplicative data: growth rates, interest rates, population growth, or any data spanning multiple orders of magnitude. Use arithmetic mean for additive data like test scores or heights.
For many values or large numbers, the product can overflow. Taking ln of each value, averaging those, then exponentiating gives the same result without overflow.