Harmonic Mean
GMAT glossary · Playbook
Definition
The rate average for equal distances (or time-weighted rates); for two speeds a and b it is 2ab/(a+b), or more generally total distance over total time.
Harmonic Mean in plain English
Pull the Harmonic Mean when the same distance is covered at different speeds, or when a rate average must weight by time. Clues include average speed for the round trip and same route each way. For two equal distances use 2ab/(a+b); more generally use total distance / total time. Arithmetic means overweight the fast leg; harmonic (or D/T) respects time spent on the slow leg. If the distances are unequal, skip the two-speed shortcut and go straight to total distance over total time. Micro-example: 60 mph going and 40 mph returning over equal distances. Harmonic mean = 2(60)(40)/(60+40) = 48 mph, not the arithmetic 50, because the slower return lasts longer.
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