Geometric — Moments

Calculates the geometric mean of a given population.

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Interface

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

using namespace Statistics::Moments;

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

The geometric mean of a sequence $x_i$ is defined by:

$$G=\sqrt[N]{\prod_{i=1}^N x_i}$$

(1)

Thus,

$$G(x_1,x_2)=\sqrt{x_1x_2}$$

(2)

$$G(x_1,x_2,x_3)=\sqrt[3]{x_1x_2x_3}$$

(3)

and so on. For $N=2$, the geometric mean is related to the arithmetic mean and harmonic mean by

$$G=\sqrt{AH}$$

(4)

where:

A = arithmetic mean and
H = harmonic mean

Example 1

#include <codecogs/statistics/moments/geometric.h>
#include <iostream>
#include<math.h>
int main() 
{
  int x[5] = {4 , 6 , 1 , 3 , 7};
  double geom = Statistics::Moments::geometric(5, x);
  std::cout << "The population mean is: " << geom << std::endl;
  return 0;
}

Output:

The population mean is: 3.47125

Parameters

the size of the population

data

the actual population data given as an array

Returns

return value the geometric mean of the given population