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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

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

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// 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;
}

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C++

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// 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;
}

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Java

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// 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. 

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Python3

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# 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)

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C#

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// 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. 

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PHP

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<?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. 
?>

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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

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// 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;
}

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C++

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// 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;
}

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Java

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// 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.  

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Python3

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# 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)

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C#

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// 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. 

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PHP

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<?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. 
?>

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2.500000

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

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