The geometric mean is also one of the three classical Pythagorean means, together with the aforementioned arithmetic mean and the harmonic mean.
32.
In population genetics, the harmonic mean is used when calculating the effects of fluctuations in generation size on the effective breeding population.
33.
This problem can be overcome by taking instead the expectation of the harmonic mean ( 1 / " x " ).
34.
Thus the " n " th harmonic mean is related to the " n " th geometric and arithmetic means.
35.
Therefore, the harmonic mean ( " H X " ) of a beta distribution with shape parameters ? and ? is:
36.
Being proportional to the harmonic mean of " A " and " B ", this formula has several applications.
37.
In this scenario, using the arithmetic or harmonic mean would change the ranking of the results depending on what is used as a reference.
38.
The " conductivity effective mass " of a semiconductor is also defined as the harmonic mean of the effective masses along the three crystallographic directions.
39.
Suppose there are " t " non-overlapping generations, then effective population size is given by the harmonic mean of the population sizes:
40.
Where p _ F is the final price of the investment and \ tilde { p } _ P is the harmonic mean of the purchase prices.
