Statistics
Geometric mean of n values
Multiply all values and take the nth root of the product.
The Formula
GM = (x1 x x2 x ... x xn)^(1/n)
Multiply all values and take the nth root of the product.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| GM | Geometric mean | same as input | The multiplicative average of the values. |
| x1 ... xn | Values | same as input | The positive numbers being averaged. |
| n | Count | unitless | How many values are being averaged. |
What Each Symbol Means
GMsame as input
Geometric mean
The multiplicative average of the values.
x1 ... xnsame as input
Values
The positive numbers being averaged.
nunitless
Count
How many values are being averaged.
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.