Harmonic Average or harmonic mean is the reciprocal of the arithmetic average of the reciprocals of the data. For example, the harmonic mean of three values x, y and z will be equivalent to 3/(1/x + 1/y + 1/z). If one of the values is zero, the result will be zero.

The harmonic average is a measure of the central location of the data. It is often appropriate when averaging ratios or rates, for example speeds.

For instance, a car travels 15 km at 20 km/hr, then another 15 km at 30 km/hr. What is the average speed?

2/(1/20 + 1/30) = 24

For instance, in this case with weights, a car travels 20 km/hr for 5 km, and when traffic clears, speeds-up to 30 km/hr for the remaining 30 km of the journey. What is the average speed?

(0.05+0.3) / (0.05/20 + 0.3/30) = 28