Mean — Moments | CodeCogs

Calculates the arithmetic mean of a given population

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Interface

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

using namespace Statistics::Moments;

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

The arithmetic mean of a set of values is the quantity commonly called the mean or the average. Given a set of samples $\{x_i\}$ the arithmetic mean is

$$\overline{x}\equiv <x>\equiv \frac{ 1}{N }\sum_{i=1 }^{N}{ x}_{ i}$$

(1)

The arithmetic mean is the special case $M_1$ of the power mean and is one of the Pythagorean means. When viewed as an estimator for the mean of the underlying distribution (known as the population mean), the arithmetic mean of a sample is called the sample mean. The arithmetic mean satisfies :

$$<cf(x)>=c<f(x)>$$

(2)

$$<f(x) + g(x)> = <f(x)> + <g(x)>$$

(3)

$$<f(x)g(y)>=<f(x)><g(y)>$$

(4)

where x and y are independent statistics. The sample mean which is the mean estimated from a statistical sample, is an unbiased estimator for the population mean.

Example 1

#include <codecogs/statistics/moments/mean.h>
#include <iostream>
int main()
{
  int x[5] = {3 , 5 , 8 , 5 , 2};
  double avg = Statistics::Moments::mean(5, x);
  std::cout << "The population mean is: " << avg << std::endl;
  return 0;
}

Output:

The population mean is: 4.6

Parameters

the size of the population

data

the actual population data given as an array

Returns

the arithmetic mean of the given population