harmonic mean

harmonic mean (plural harmonic means)

1. (mathematics) A type of measure of central tendency calculated as the reciprocal of the mean of the reciprocals, ie, ${\displaystyle H={n \over {1 \over x_{1}}+{1 \over x_{2}}+\cdots {1 \over x_{n}}}}$

   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 2n-gons, respectively, along that same circle. (This is Archimedes' Recurrence Formula.)

• (statistics): measure of central tendency

• arithmetic mean
• contraharmonic mean
• geometric mean
• quadratic mean