Statistics
Weighted harmonic mean over unequal legs
Total distance over total time, the correct average speed for unequal legs.
The Formula
H = (d1 + d2 + ... + dn) / (d1/x1 + d2/x2 + ... + dn/xn)
Total distance over total time, the correct average speed for unequal legs.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| H | Average rate | same as input | The overall rate across all legs. |
| di | Leg size | unitless | The distance, work or weight of each leg. |
| xi | Rate | same as input | The rate for that leg. |
What Each Symbol Means
Hsame as input
Average rate
The overall rate across all legs.
diunitless
Leg size
The distance, work or weight of each leg.
xisame as input
Rate
The rate for that leg.
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.