Enter a set of numbers to compute the harmonic mean as the reciprocal of the arithmetic mean of reciprocals, suited to rates and unit prices.
倒数的算术平均之倒数，适合速率。
| Item | Formula / Note | Source / Standard |
|---|---|---|
| Harmonic mean | H = n / sum(1 / x_i) | ISO 3534-1:2006, Statistics - Vocabulary and symbols |
| Mean inequality | H <= G <= A, with equality only when all values are equal | Hardy GH, Littlewood JE, Polya G, Inequalities (1934) |
| Equal-amount average cost | Average price under equal-amount purchases = n / sum(1 / p_i) | Hardy GH et al., Inequalities (1934), classical application |
| Average speed over equal distances | v = 2·v1·v2 / (v1 + v2) for two legs of equal distance | Hardy GH et al., Inequalities (1934), classical kinematics relation |