CodeCogs

Calculates the harmonic mean of a given population.

View versions (1)

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 = 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

the size of the population

data

the actual population data given as an array

Returns

the harmonic mean of a given population

Harmonic

Interface

Example 1

Parameters

Returns