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Program to calculate Root Mean Square

Given an array of N numbers. The task is to calculate the Root Mean Square(RMS) of the given numbers.
Examples

```Input: arr[] = {1, 2, 3, 4, 5}
Output: 3.31662

Input: arr[] = {10, 4, 6, 8}
Output: 7.34847```

Approach: The Root Mean Square value of N numbers x1,x2,x3,…..xn can be given as,

RMS method first calculates the square of each number and then calculate the mean and finally calculate the square root of the mean.
Below is the program to find RMS of N numbers:

C++

 `// CPP program to calculate Root Mean Square``#include ``using` `namespace` `std;` `// Function that Calculate Root Mean Square``float` `rmsValue(``int` `arr[], ``int` `n)``{``    ``int` `square = 0;``    ``float` `mean = 0.0, root = 0.0;` `    ``// Calculate square.``    ``for` `(``int` `i = 0; i < n; i++) {``        ``square += ``pow``(arr[i], 2);``    ``}` `    ``// Calculate Mean.``    ``mean = (square / (``float``)(n));` `    ``// Calculate Root.``    ``root = ``sqrt``(mean);` `    ``return` `root;``}` `// Driver code``int` `main()``{``    ``int` `arr[] = { 10, 4, 6, 8 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``cout << rmsValue(arr, n);` `    ``return` `0;``}`

Java

 `// Java program to calculate``// Root Mean Square` `class` `GFG``{` `// Function that Calculate Root``// Mean Square``static` `float` `rmsValue(``int` `arr[], ``int` `n)``{``    ``int` `square = ``0``;``    ``float` `mean = ``0``;``    ``float` `root = ``0``;` `    ``// Calculate square.``    ``for``(``int` `i = ``0``; i < n; i++)``    ``{``        ``square += Math.pow(arr[i], ``2``);``    ``}``    ` `    ``// Calculate Mean.``    ``mean = (square / (``float``) (n));` `    ``// Calculate Root.``    ``root = (``float``)Math.sqrt(mean);` `    ``return` `root;``}`  `// Driver Code``public` `static` `void` `main(String args[])``{``    ``int` `arr[] = { ``10``, ``4``, ``6``, ``8``};``    ` `    ``int` `n = arr.length;``    ` `    ``System.out.println(rmsValue(arr, n));``}``}` `// This code is contributed by ANKITRAI1`

Python3

 `#Python3 program to calculate Root Mean Square` `import` `math``#Function that Calculate Root Mean Square``def` `rmsValue(arr, n):``    ``square ``=` `0``    ``mean ``=` `0.0``    ``root ``=` `0.0``    ` `    ``#Calculate square``    ``for` `i ``in` `range``(``0``,n):``        ``square ``+``=` `(arr[i]``*``*``2``)``    ` `    ``#Calculate Mean``    ``mean ``=` `(square ``/` `(``float``)(n))``    ` `    ``#Calculate Root``    ``root ``=` `math.sqrt(mean)``    ` `    ``return` `root` `#Driver code``if` `__name__``=``=``'__main__'``:``    ``arr ``=` `[``10``, ``4``, ``6``, ``8``]``    ``n ``=` `len``(arr)``    ``print``(rmsValue(arr, n))` `#This code is contributed by Shashank_Sharma`

C#

 `// C# program to calculate``// Root Mean Square``using` `System;``class` `GFG``{` `// Function that Calculate``// Root Mean Square``static` `float` `rmsValue(``int``[] arr, ``int` `n)``{``    ``int` `square = 0;``    ``float` `mean = 0;``    ``float` `root = 0;` `    ``// Calculate square.``    ``for``(``int` `i = 0; i < n; i++)``    ``{``        ``square += (``int``)Math.Pow(arr[i], 2);``    ``}``    ` `    ``// Calculate Mean.``    ``mean = (square / (``float``) (n));` `    ``// Calculate Root.``    ``root = (``float``)Math.Sqrt(mean);` `    ``return` `root;``}` `// Driver Code``public` `static` `void` `Main()``{``    ``int``[] arr = {10, 4, 6, 8};``    ` `    ``int` `n = arr.Length;``    ` `    ``Console.Write(rmsValue(arr, n));``}``}` `// This code is contributed``// by ChitraNayal`

PHP

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Javascript

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Output:

`7.34847`

Time Complexity: O(n) where n is size of given array, because for loop would run for all elements of array
Auxiliary Space: O(1)

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