# Average of Squares of Natural Numbers

• Last Updated : 24 Mar, 2021

Given a number n, find the average of square of natural Numbers till n
Examples :

```Input : n = 2
Output :2.5
12 + 22 = 2.5

Input  : n = 3
Output : 4.666667
12 + 22 + 32 = 4.666667```

Naive approach :
A naive approach will be to run a loop from 1 to n and and find the average of sum up all the squares.

## C

 `// C program to calculate 1^2+2^2+3^2+... average``// of square number``#include ` `// Function to calculate  average of square number``float` `AvgofSquareN(``int` `n)``{``    ``float` `sum = 0;``    ``for` `(``int` `i = 1; i <= n; i++)``        ``sum += (i * i);``    ``return` `sum/n;``}` `// Driver code``int` `main()``{``    ``int` `n = 2;``    ``printf``(``"%f"``, AvgofSquareN(n));``    ``return` `0;``}`

## C++

 `// C++ program to calculate 1^2+2^2+3^2+...``// average of square number``#include``using` `namespace` `std;` `// Function to calculate average of squares``float` `AvgofSquareN(``int` `n)``{``    ``float` `sum = 0;``    ``for` `(``int` `i = 1; i <= n; i++)``        ``sum += (i * i);``    ``return` `sum/n;``}` `// Driver code``int` `main()``{``    ``int` `n = 2;``    ``cout << AvgofSquareN(n) ;``    ``return` `0;``}`

## Java

 `// Java program to calculate 1^2+2^2+3^2+``// ... average of square number``import` `java.io.*;` `public` `class` `GFG{``    ` `// Function to calculate average``// of square number``static` `float` `AvgofSquareN(``int` `n)``{``    ``float` `sum = ``0``;``    ``for` `(``int` `i = ``1``; i <= n; i++)``        ``sum += (i * i);``    ``return` `sum / n;``}` `// Driver code``static` `public` `void` `main (String[] args)``{``    ``int` `n = ``2``;``    ``System.out.println(AvgofSquareN(n));` `}``}` `// This code is contributed by vt_m.`

## Python3

 `# Python program to``# calculate 1^2+2^2+3^2+...``# average of square number` `# Function to calculate``# average of square number``def` `AvgofSquareN(n) :` `    ``sum` `=` `0``    ``for` `i ``in` `range``(``1``, n ``+` `1``) :``        ``sum` `+``=` `(i ``*` `i)``    ``return` `sum``/``n` `# Driver code``n ``=` `2``print` `(AvgofSquareN(n))``    ` `# This code is contributed by``# Manish Shaw(manishshaw1)`

## C#

 `// C# program to calculate 1^2+2^2+3^2+``// ... average of square number``using` `System;` `public` `class` `GFG{``    `  `// Function to calculate average``// of square number``static` `float` `AvgofSquareN(``int` `n)``{``    ``float` `sum = 0;``    ``for` `(``int` `i = 1; i <= n; i++)``        ``sum += (i * i);``    ``return` `sum / n;``}` `// Driver code``static` `public` `void` `Main (String []args)``{``    ``int` `n = 2;``    ``Console.WriteLine(AvgofSquareN(n));``    ` `}``}` `// This code is contributed by vt_m.`

## PHP

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## Javascript

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Output :

`2.500000`

Time Complexity: O(n)
Space Complexity: O(1)
Efficient Approach : Sum of squares of natural numbers (n + 1)(2n + 1) / 6. Therefore average is n(n + 1)(2n + 1) / 6 * n = (n + 1)(2n + 1) / 6.

## C

 `// C program to get the  Average of Square``// of first n natural numbers``#include ` `float` `AvgofSquareN(``int` `n)``{``    ``return` `(``float``)((n + 1) * (2 * n + 1)) / 6;``}` `// Driver Code``int` `main()``{``    ``int` `n = 10;``    ``printf``(``"%f"``, AvgofSquareN(n));``    ``return` `0;``}`

## C++

 `// C++ program to get the  Average of Square``// of first n natural numbers``#include``using` `namespace` `std;` `float` `AvgofSquareN(``int` `n)``{``    ``return` `(``float``)((n + 1) * (2 * n + 1)) / 6;``}` `// Driver Code``int` `main()``{``    ``int` `n = 10;``    ``cout << AvgofSquareN(n) ;``    ``return` `0;``}`

## Java

 `// Java program to get the Average of``// square of first n natural numbers``import` `java.io.*;` `public` `class` `GFG{` `// Function to get the average``static` `float` `AvgofSquareN(``int` `n)``{``    ``return` `(``float``)((n + ``1``) * (``2` `*``                    ``n + ``1``)) / ``6``;``}` `// Driver Code``static` `public` `void` `main (String[] args)``{``    ``int` `n = ``2``;``    ``System.out.println(AvgofSquareN(n));` `}``}` `// This code is contributed by vt_m. `

## Python3

 `# PHP program to get the Average of``# Square of first n natural numbers`` ` `def` `AvgofSquareN(n) :` `    ``return` `((n ``+` `1``) ``*` `(``2` `*` `n ``+` `1``)) ``/` `6``;` `# Driver Code``n ``=` `2``;``print` `(AvgofSquareN(n));`` ` `# This code is contributed by Manish Shaw``# (manishshaw1)`

## C#

 `// C# program to get the Average of``// squareof first n natural numbers``using` `System;` `public` `class` `GFG{` `// Function to calculate average``static` `float` `AvgofSquareN(``int` `n)``{``    ``return` `(``float``)((n + 1) * (2 *``                    ``n + 1)) / 6;``}` `// Driver Code``static` `public` `void` `Main (String []args)``{``    ``int` `n = 2;``    ``Console.WriteLine(AvgofSquareN(n));``}``}` `// This code is contributed by vt_m.`

## PHP

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## Javascript

 ``

`2.500000`

Time Complexity: O(1)
Space Complexity: O(1)

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