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what is weighted harmonic mean. The harmonic mean formula above assumes each rate has produced the same output ie the same distance was travelled at each of the different rates or the same amount of liquid was pumped at each of the different rates. Note that example 2 had equal times for both drivers and this is why the arithmetic mean was correct.
The paper advocates the use of the classic harmonic mean when the need is for an equal-dollar-weighted average and the weighted-average harmonic mean when the need is for an index style market-weighted average. And if the time spent at each speed is equal then it is the arithmetic mean of speeds. X_i the point in a dataset.
The harmonic mean is.
Harmonic Mean 2 x1 x2 x1 x2. The harmonic mean is equivalent to the weighted arithmetic mean of rate of travel where values are weighted by relative time spent traveling. Weighted Harmonic Mean w_i w_ix_i Where. It is a weighted arithmetic mean of speeds weighted by time.