Geometric mean (Two Methods) - GeeksforGeeks

06 May, 2021
Given an array of n elements, we need to find the geometric mean of the numbers. Generally geometric mean of n numbers is the nth 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++
Java
Python
C#
PHP
Javascript
// 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 functionint main(){    int arr[] = { 1, 2, 3, 4, 5, 6, 7, 8 };    int n = sizeof(arr) / sizeof(arr[0]);    cout << geometricMean(arr, n);    return 0;}
// 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 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 functionarr = [ 1, 2, 3, 4, 5, 6, 7, 8]n = len(arr) # to print 6 digits after decimalprint ('{0:.6f}'.format(geometricMean(arr, n)))   # This code is contributed by Nikita Tiwari
// 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// 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.?>
<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
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++
Java
Python3
C#
PHP
Javascript
// 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 functionint 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 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.
# 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 Codearr= [ 1, 2, 3, 4, 5, 6, 7, 8 ];n = len(arr); # function callprint(geometricMean(arr, n)); # This code is contributed by mits.
// 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// 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.?>
<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
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