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 <stdio.h> 
  
// 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<bits/stdc++.h> 
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

<?php 
// PHP program to calculate 1^2+2^2+3^2+...  
// average of square number 
  
// Function to calculate average 
// of square number 
function AvgofSquareN( $n) 
{ 
    $sum = 0; 
    for ($i = 1; $i <= $n; $i++) 
        $sum += ($i * $i); 
    return $sum/$n; 
} 
  
    // Driver code 
    $n = 2; 
    echo(AvgofSquareN($n)); 
      
// This code is contributed by vt_m.  
?> 

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 <stdio.h> 
  
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<bits/stdc++.h> 
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

<?php 
// PHP program to get the Average of  
// Square of first n natural numbers 
  
function AvgofSquareN( $n) 
{ 
    return (($n + 1) * (2 * $n + 1)) / 6; 
} 
  
    // Driver Code 
    $n = 2; 
    echo(AvgofSquareN($n)); 
  
// This code is contributed by vt_m.  
?> 

2.500000

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

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Related Articles

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

C

C++

Java

Python3

C#

PHP

C

C++

Java

Python3

C#

PHP