Harmonic mean is the reciprocal of the arithmetic mean of reciprocals. Formula: H = n / (1/x₁ + 1/x₂ + ... + 1/xₙ). Used for rates, speeds, and ratios.
When should I use harmonic mean?▼
Use harmonic mean for data involving rates, speeds, times, and ratios. It gives equal weight to each unit of measure, unlike arithmetic mean.
Can harmonic mean handle zero or negative numbers?▼
No, harmonic mean is only defined for positive numbers. Zero would cause division by zero, and negative values would produce meaningless results.
What is the relationship between the three means?▼
For positive numbers: Arithmetic Mean ≥ Geometric Mean ≥ Harmonic Mean (AM-GM-HM inequality). Equality only when all numbers are equal.
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