# Geometric mean (Two Methods)

• Difficulty Level : Easy
• Last Updated : 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++

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

 ``

## Javascript

 `   `

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++

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

 ``

## Javascript

 ``

Output:

`3.76435`

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