Statistics
Logarithm form
Averaging logarithms avoids overflow when the product is very large.
The Formula
GM = exp( (ln x1 + ln x2 + ... + ln xn) / n )
Averaging logarithms avoids overflow when the product is very large.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| GM | Geometric mean | same as input | The multiplicative average. |
| ln | Natural logarithm | unitless | The log base e of each value. |
| exp | Exponential | unitless | Raises e to the averaged logarithm. |
What Each Symbol Means
GMsame as input
Geometric mean
The multiplicative average.
lnunitless
Natural logarithm
The log base e of each value.
expunitless
Exponential
Raises e to the averaged logarithm.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate a geometric mean page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate A Geometric Mean, filed under Math. Every number the guide produces comes from substituting into this one line.