harmonic meanharmonic mean
a number associated with a set of numbers, that is equal to the number of numbers divided by the sum of the reciprocals of the numbers (h = n ÷ ( + + + …)) (Ex.: for , , and , h = 3 ÷ (2 + 3 + 4) = ; for and , h = 2 ÷ (2 + 3) = )
The reciprocal of the arithmetic mean of the reciprocals of a specified set of numbers.
(plural harmonic means)
- (mathematics) A type of measure of central tendency calculated as the reciprocal of the mean of the reciprocals, ie,
- If an and bn denote the perimeters of inscribed and circumscribed regular n-gons, respectively, along some circle then the harmonic mean and geometric mean of those two perimeters yield the perimeters of the inscribed and circumscribed regular 2n-gons, respectively, along that same circle. (This is Archimedes' Recurrence Formula.)