Harmonic

Calculates the harmonic mean of a given population.

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Interface
Harmonic
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Interface

C++

Harmonic

template<class T> doubleharmonic(	int	`n`
	T*	`data`	)

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

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

(2)

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

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

(3)

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

(4)

and so on.

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

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

(5)

The harmonic mean is the special case $\inline M_{-1}$ 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 = Stats::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

n	the size of the population
data	the actual population data given as an array

Returns

the harmonic mean of a given population

Authors

Anca Filibiu (August 2005)

Source Code

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