Understand the subject
What is the harmonic mean?
The harmonic mean is a reciprocal center. It gives greater influence to smaller positive values because it averages their reciprocals first.
It is useful for rates when equal amounts of the numerator quantity are involved—for example, speeds over equal distances.
The relationship
The defining equation
H = n / Σ(1/xᵢ)
xᵢ are positive rates or ratios, n is their count, and H is the harmonic mean.
See the structure
Turn rates into time per unit
60 km/h1/60 h per km40 km/h1/40 h per kmaverage time per km → 48 km/h
Worked example
Equal distances at 60 and 40 km/h
H = 2 ÷ (1/60 + 1/40) = 48 km/h
Interpret with care
What the result does—and does not—mean
Equal time at each speed would require an arithmetic mean instead. The weight must match what is held equal.