The harmonic mean (HM) is the reciprocal of the arithmetic mean of the reciprocals of the observations — the correct average to use when the data are rates or ratios (speed, price per unit, etc.).

The governing formula

For just two values it simplifies to $HM = \dfrac{2x_1 x_2}{x_1 + x_2}$.

Why it works

Rates share a common numerator (distance, money) but different denominators (time, quantity). Adding reciprocals correctly combines the denominators, so HM answers 'what single rate gives the same total?'.

Worked illustration …