Statistics
Harmonic mean of n values
Add the reciprocals of all values, then divide the count by that sum.
The Formula
H = n / (1/x1 + 1/x2 + ... + 1/xn)
Add the reciprocals of all values, then divide the count by that sum.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| H | Harmonic mean | same as input | The rate-aware average of the values. |
| n | Count | unitless | How many values are being averaged. |
| xi | Values | same as input | The positive numbers being averaged. |
What Each Symbol Means
Hsame as input
Harmonic mean
The rate-aware average of the values.
nunitless
Count
How many values are being averaged.
xisame as input
Values
The positive numbers 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 harmonic 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 Harmonic Mean, filed under Math. Every number the guide produces comes from substituting into this one line.