## harmonic 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 ÷ (1/a + 1/b)) (Ex.: for , , and , h = 3 ÷ (2 + 3 + 4) = or for and , h = 2 ÷ (2 + 3) = )

## harmonic mean

noun

The reciprocal of the arithmetic mean of the reciprocals of a specified set of numbers.

## harmonic mean

Noun

(*plural* harmonic means)

- (mathematics) A type of measure of central tendency calculated as the reciprocal of the mean of the reciprocals, ie,
- If
*a*_{n}and*b*_{n}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 2*n*-gons, respectively, along that same circle. (This is Archimedes' Recurrence Formula.)

- If