Geometric mean (Two Methods)

Given an array of n elements, we need to find the geometric mean of the numbers. Generally geometric mean of n numbers is the n^th root of their product. 

   If there are n elements x1, x2, x3, . . ., xn
   in an array and if we want to calculate the 
   geometric mean of the array elements is
   Geometric mean = (x1 * x2 * x3 * . . . * xn)1/n 

Examples:

Input : arr[] = {1, 2, 3, 4, 5, 6, 7, 8}
Output : 3.76435
        = (1 * 2 * 3 * 4 * 5 * 6 * 7 * 8)1/8
        = 403201/8
        = 3.76435

Input : arr[] = {15, 12, 13, 19, 10}
Output : 13.447
        = (15 * 12 * 13 * 19 * 10)1/5
        = 4446001/5
        = 13.477

A simple solution is to multiply all numbers first, then find (1/n)-th power of the multiplication. 

C++

// Program to calculate the geometric mean
// of the given array elements.
#include <bits/stdc++.h>
using namespace std;

// function to calculate geometric mean
// and return float value.
float geometricMean(int arr[], int n)
{
    // declare product variable and
    // initialize it to 1.
    float product = 1;

    // Compute the product of all the
    // elements in the array.
    for (int i = 0; i < n; i++)
        product = product * arr[i];

    // compute geometric mean through formula
    // pow(product, 1/n) and return the value
    // to main function.
    float gm = pow(product, (float)1 / n);
    return gm;
}

// Driver function
int main()
{
    int arr[] = { 1, 2, 3, 4, 5, 6, 7, 8 };
    int n = sizeof(arr) / sizeof(arr[0]);
    cout << geometricMean(arr, n);
    return 0;
}

Java

// Program to calculate the geometric mean
// of the given array elements.
import java.math.*;

class GFG{

    // function to calculate geometric mean
    // and return float value.
    static float geometricMean(int arr[], int n)
    {
        // declare product variable and
        // initialize it to 1.
        float product = 1;

        // Compute the product of all the
        // elements in the array.
        for (int i = 0; i < n; i++)
            product = product * arr[i];

        // compute geometric mean through
        // formula pow(product, 1/n) and
        // return the value to main function.
        float gm = (float)Math.pow(product, (float)1 / n);
        return gm;
    }

    // Driver function
    public static void main(String args[])
    {
        int arr[] = { 1, 2, 3, 4, 5, 6, 7, 8 };
        int n = arr.length ;
        System.out.println(geometricMean(arr, n));
    }
}

/*This code is contributed by Nikita Tiwari*/

Python

# Python Program to calculate the
# geometric mean of the given
# array elements.
import math

# function to calculate geometric
# mean and return float value.
def geometricMean(arr, n) :

    # declare product variable and
    # initialize it to 1.
    product = 1

    # Compute the product of all the
    # elements in the array.
    for i in range(0,n) :
        product = product * arr[i]

    # compute geometric mean through
    # formula pow(product, 1/n) and
    # return the value to main function.
    gm = (float)(math.pow(product, (1 / n)))
    return (float)(gm)


# Driver function
arr = [ 1, 2, 3, 4, 5, 6, 7, 8]
n = len(arr)

# to print 6 digits after decimal
print ('{0:.6f}'.format(geometricMean(arr, n)))


# This code is contributed by Nikita Tiwari

C#

// Program to calculate the geometric mean
// of the given array elements.
using System;

class GFG{

    // function to calculate geometric mean
    // and return float value.
    static float geometricMean(int []arr, int n)
    {
        // declare product variable and
        // initialize it to 1.
        float product = 1;

        // Compute the product of all the
        // elements in the array.
        for (int i = 0; i < n; i++)
            product = product * arr[i];

        // compute geometric mean through
        // formula pow(product, 1/n) and
        // return the value to main function.
        float gm = (float)Math.Pow(product, (float)1 / n);
        return gm;
    }

    // Driver function
    public static void Main()
    {
        int []arr = { 1, 2, 3, 4, 5, 6, 7, 8 };
        int n = arr.Length ;
        Console.WriteLine(geometricMean(arr, n));
    }
}

/*This code is contributed by vt_m*/

PHP

<?php
// Program to calculate the geometric mean
// of the given array elements.

// function to calculate geometric mean
// and return float value.
function geometricMean($arr, $n)
{

    // declare product variable and
    // initialize it to 1.
    $product = 1;

    // Compute the product of all the
    // elements in the array.
    for ($i = 0; $i < $n; $i++)
        $product = $product * $arr[$i];

    // compute geometric mean through formula
    // pow(product, 1/n) and return the value
    // to main function.
    $gm = pow($product, (float)(1 / $n));
    return $gm;
}

// Driver Code
$arr = array(1, 2, 3, 4, 5, 6, 7, 8);
$n = sizeof($arr);
echo(geometricMean($arr, $n));

// This code is contributed by Ajit.
?>

Javascript

<script>
// Javascript program to calculate the geometric mean
// of the given array elements.

    // function to calculate geometric mean
    // and return float value.
    function geometricMean(arr, n)
    {
        // declare product variable and
        // initialize it to 1.
        let product = 1;

        // Compute the product of all the
        // elements in the array.
        for (let i = 0; i < n; i++)
            product = product * arr[i];

        // compute geometric mean through
        // formula pow(product, 1/n) and
        // return the value to main function.
        let gm = Math.pow(product, 1 / n);
        return gm;
    }

// driver function

        let arr = [ 1, 2, 3, 4, 5, 6, 7, 8 ];
        let n = arr.length ;
        document.write(geometricMean(arr, n));

   // This code is contributed by code_hunt.
</script>

Output: 

3.76435

Time Complexity: O(n) where n is size of given array

Auxiliary Space: O(1)

The above solution simply causes overflow. A better solution is to use log. There are n numbers and we need to calculate geometric mean using the formula : 

Geometric mean = Antilog((log(x1) + log(x2) +
                 log(x3) + . . . + log(xn))/n)  

For calculating the Antilog in programming we use exponent function (exp()). 

C++

// Program to calculate the geometric mean
// of the given array elements.
#include <bits/stdc++.h>
using namespace std;

// function to calculate geometric mean
// and return float value.
float geometricMean(int arr[], int n)
{
    // declare sum variable and
    // initialize it to 1.
    float sum = 0;

    // Compute the sum of all the
    // elements in the array.
    for (int i = 0; i < n; i++)
        sum = sum + log(arr[i]);

    // compute geometric mean through formula
    // antilog(((log(1) + log(2) + . . . + log(n))/n)
    // and return the value to main function.
    sum = sum / n;

    return exp(sum);
}

// Driver function
int main()
{
    int arr[] = { 1, 2, 3, 4, 5, 6, 7, 8 };
    int n = sizeof(arr) / sizeof(arr[0]);
    // function call
    cout << geometricMean(arr, n);
    return 0;
}

Java

// Java Program to calculate the geometric mean
// of the given array elements.
import java.io.*;

class GFG
{

    // function to calculate geometric mean
    // and return float value.
    static float geometricMean(int []arr, int n)
    {
        // declare sum variable and
        // initialize it to 1.
        float sum = 0;

        // Compute the sum of all the
        // elements in the array.
        for (int i = 0; i < n; i++)
            sum = sum + (float)Math.log(arr[i]);

        // compute geometric mean through formula
        // antilog(((log(1) + log(2) + . . . + log(n))/n)
        // and return the value to main function.
        sum = sum / n;

        return (float)Math.exp(sum);
    }

    // Driver function
    public static void main (String[] args)
    {
        int []arr = { 1, 2, 3, 4, 5, 6, 7, 8 };
        int n = arr.length;

        // function call
        System.out.println(geometricMean(arr, n));

    }
}

// This code is contributed by vt_m.

Python3

# Program to calculate the
# geometric mean of the
# given array elements.
import math

# function to calculate
# geometric mean and
# return float value.
def geometricMean(arr, n):

    # declare sum variable and
    # initialize it to 1.
    sum = 0;

    # Compute the sum of all
    # the elements in the array.
    for i in range(n):
        sum = sum + math.log(arr[i]);

    # compute geometric mean
    # through formula antilog
    # (((log(1) + log(2) + . .
    # ... + log(n))/n)
    # and return the value to
    # main function.
    sum = sum / n;

    return math.exp(sum);

# Driver Code
arr= [ 1, 2, 3, 4, 5, 6, 7, 8 ];
n = len(arr);

# function call
print(geometricMean(arr, n));

# This code is contributed by mits.

C#

// Program to calculate the geometric mean
// of the given array elements.
using System;

class GFG {

    // function to calculate geometric mean
    // and return float value.
    static float geometricMean(int []arr, int n)
    {
        // declare sum variable and
        // initialize it to 1.
        float sum = 0;

        // Compute the sum of all the
        // elements in the array.
        for (int i = 0; i < n; i++)
            sum = sum + (float)Math.Log(arr[i]);

        // compute geometric mean through formula
        // antilog(((log(1) + log(2) + . . . + log(n))/n)
        // and return the value to main function.
        sum = sum / n;

        return (float)Math.Exp(sum);
    }

    // Driver function
    public static void Main ()
    {
        int []arr = { 1, 2, 3, 4, 5, 6, 7, 8 };
        int n = arr.Length;

        // function call
        Console.WriteLine(geometricMean(arr, n));

    }
}

// This code is contributed by vt_m.

PHP

<?php
// Program to calculate the geometric mean
// of the given array elements.

// function to calculate geometric mean
// and return float value.
function geometricMean($arr, $n)
{

    // declare sum variable and
    // initialize it to 1.
    $sum = 0;

    // Compute the sum of all the
    // elements in the array.
    for($i = 0; $i < $n; $i++)
        $sum = $sum + log($arr[$i]);

    // compute geometric mean
    // through formula
    // antilog(((log(1) + log(2) +
    // . . . + log(n))/n)
    // and return the value
    $sum = $sum / $n;

    return exp($sum);
}

    // Driver Code
    $arr = array(1, 2, 3, 4, 5, 6, 7, 8);
    $n = count($arr);

    // function call
    echo geometricMean($arr, $n);

// This code is contributed by anuj_67.
?>

Javascript

<script>

// Program to calculate the geometric mean
// of the given array elements.


    // function to calculate geometric mean
    // and return float value.

    function geometricMean(arr, n)
    {
        // declare sum variable and
        // initialize it to 1.
        var sum = 0;

        // Compute the sum of all the
        // elements in the array.
        for (var i = 0; i < n; i++)
            sum = sum + Math.log(arr[i]);

        // compute geometric mean through formula
        // antilog(((log(1) + log(2) + . . . + log(n))/n)
        // and return the value to main function.

        sum = sum / n;

        return Math.exp(sum);
    }

    // Driver function

        var arr = [ 1, 2, 3, 4, 5, 6, 7, 8 ];
        var n = arr.length;

        // function call
        document.write(geometricMean(arr, n).toFixed(5));

 // This code is contributed by bunnyram19.
</script>

Output:

3.76435

Time Complexity: O(n)

Auxiliary Space: O(1)
This article is contributed by Dharmendra Kumar. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.