KnowraHarmonic meanLinked fromLinked fromThe 8 pages that link to Harmonic mean, each with the reason it gives.All 8Broader topic 1Related 3Compared with 4Arithmetic meanCompared with: It is often appropriate for averaging rates with equal quantities, unlike the ordinary mean.Geometric meanCompared with: It is another classical mean, suited to rates and reciprocal quantities.ReciprocalRelated: Its definition turns each input into a reciprocal before averaging.Sample meanCompared with: It gives a different average, often appropriate for rates with a shared numerator.Weighted averageCompared with: It is suited to rates and ratios, where an arithmetic weighted average may mislead.Nesbitt's inequalityRelated: Nesbitt's bound is equivalent to saying the harmonic mean of x, y, z does not exceed their arithmetic mean.Shapiro inequalityRelated: Reciprocal-sum estimates related to harmonic means appear in proofs of ratio inequalities.QM–AM–GM–HM inequalitiesBroader topic: It is the smallest mean in the chain.