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Average of Squares of Natural Numbers
• Last Updated : 20 Jun, 2020

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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

 ` `

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

 ` `

```2.500000
```

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

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