Calculate the geometric mean of a list of numbers - the right average for growth rates and ratios.
The geometric mean is the correct way to average rates of change, ratios, or percentages - such as year-over-year investment returns - because it accounts for compounding, unlike a simple arithmetic average.
Geometric Mean = (x₁ × x₂ × ... × xₙ)^(1/n)
The geometric mean of 4, 8, and 16 is 8 - notice it's lower than the arithmetic mean of 9.33, which is typical whenever the numbers vary.
It's the nth root of the product of n numbers: geometric mean = (x1 × x2 × ... × xn)^(1/n).
Arithmetic mean adds values and divides by count; geometric mean multiplies values and takes a root, making it better suited for rates of change, ratios, and growth rates.
Geometric mean is preferred for averaging things like investment returns over multiple periods, since it correctly accounts for compounding effects that a simple average would distort.