Harmonic — Moments

Calculates the harmonic mean of a given population.

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Interface

#include <codecogs/statistics/moments/harmonic.h>

using namespace Statistics::Moments;

template<class T> double harmonic(int n, T *data)

The harmonic mean of N numbers $x_i$ (where, $i=1,2...,N$) is defined by

$$H=\frac{n}{\sum_{i=1}^N\frac{1}{x_i}}$$

(1)

The special cases of $N=2$ and $N=3$ are therefore given by

$$H(x_1,x_2)=\frac{2x_1x_2}{x_1+x_2}$$

(2)

$$H(x_1,x_2,x_3)=\frac{3x_1x_2x_3}{x_1x_2+x_1x_3+x_2x_3},$$

(3)

and so on.

For $N=2$, the harmonic mean is related to the arithmetic mean, A, and the geometric mean, G, by

$$H=\frac{G^2}{A}$$

(4)

The harmonic mean is the special case $M_{-1}$ of the power mean and is one of the Pythagorean means.

Example 1

#include <codecogs/statistics/moments/harmonic.h>
#include <iostream>
int main()
{
  double x[4] = {3.5 , 6.5  , 5.9 , 8.8};
  double harm = Statistics::Moments::harmonic<double>(4, x);
  std::cout << "The population harmonic mean is: " << harm << std::endl;
  return 0;
}

Output:

The population harmonic mean is:5.53489

Parameters

the size of the population

data

the actual population data given as an array

Returns

the harmonic mean of a given population