Why do we need harmonic mean , how it can give better precision in specific situations. Please justify situations where harmonic mean is better than arithmetic mean.
Let's look at this problem?
A Car going to and fro @ 4km/hr , 3 km/hr and 5km/hr.
In this case, arithmetic mean gives 4 km/hr and harmonic mean gives 3.82..km/hr.
Though defitintion sugeests harmonic mean should be used when distance is the same and different speeds.
How do you justify 3.82 (harmonic mean)is a more exact average than 4(arithmetic mean.)