Program for weighted mean of natural numbers.

There are given an array of natural numbers and another array with corresponding weight of the number. Then we have to calculate the weighted mean. 

Where x (bar) is called the weighted mean, x[i] is the elements of array, and W[i] is the weight of elements of array x[i].

Examples:

Input : 
X[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
W[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} 
weighted mean 
= (W[0] * X[0] + W[1] * X[1] + W[2] * X[2] + . . . +
   W[n-1] * X[n-1]) / (W[0] + W[1] + W[2] + . . . + W[n-1])
= (1 * 1 + 2 * 2 + 3 * 3 + . . . + 10 * 10) /
  (1 + 2 + 3 + . . . + 10)
= 385 / 55 = 7
Output : 7

Input : 
X[] = {3, 4, 5, 6, 7}
W[] = {4, 5, 6, 7, 8}
weighted mean 
= (W[0] * X[0] + W[1] * X[1] + W[2] * X[2] + . . . +
   W[n-1] * X[n-1]) / (W[0] + W[1] + W[2] + . . . + W[n-1])
= (3 * 4 + 4 * 5 + 5 * 6 + 6 * 7 + 7 * 8) / 
  (4 + 5 + 6 + 7 + 8)
= 160 / 30 = 5.33333
Output : 5.33333

Implementation: A simple solution to solve weighed mean. 

C++

// Program to find weighted mean of
// natural numbers.
#include<bits/stdc++.h>
using namespace std;

// Function to calculate weighted mean.
float weightedMean(int X[], int W[], int n)
{
    int sum = 0, numWeight = 0;

    for (int i = 0; i < n; i++)
    {
        numWeight = numWeight + X[i] * W[i];
        sum = sum + W[i];
    }

    return (float)numWeight / sum;
}

// Driver program to test the function.
int main()
{
    // Take num array and corresponding weight
    // array and initialize it.
    int X[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
    int W[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};

    // Calculate the size of array.
    int n = sizeof(X)/sizeof(X[0]);
    int m = sizeof(W)/sizeof(W[0]);

    // Check the size of both array is equal or not.
    if (n == m)
        cout << weightedMean(X, W, n);
    else
        cout << "-1";
    return 0;
}

Java

// JAVA Program to find weighted mean
// of natural numbers.

class GFG {

    // Function to calculate weighted mean.
    static float weightedMean(int X[], int W[],
                                        int n)
    {
        int sum = 0, numWeight = 0;

        for (int i = 0; i < n; i++)
        {
            numWeight = numWeight + X[i] * W[i];
            sum = sum + W[i];
        }

        return (float)(numWeight) / sum;
    }

    // Driver program to test the function.
    public static void main(String args[])
    {
        // Take num array and corresponding
        // weight array and initialize it.
        int X[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
        int W[] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};

        // Calculate the size of array.
        int n = X.length;
        int m = W.length;

        // Check the size of both array is
        // equal or not.
        if (n == m)
            System.out.println(weightedMean(X, W, n));
        else
            System.out.println("-1" );

    }
}

/*This code is contributed by Nikita Tiwari.*/

Python

# Python Program to find weighted mean of
# natural numbers.

# Function to calculate weighted mean.
def weightedMean(X,W,n) :
    sum = 0
    numWeight = 0
    i = 0
    while  i < n :

        numWeight = numWeight + X[i] * W[i]
        sum = sum + W[i]
        i = i + 1

    return (float)(numWeight / sum)


# Driver program to test the function.

# Take num array and corresponding weight
# array and initialize it.
X = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
W = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]

# Calculate the size of array.
n = len(X)
m = len(W)

# Check the size of both array is equal or not.
if (n == m) :
    print weightedMean(X, W, n)
else :
    print "-1"

# This code is contributed by Nikita Tiwari.

C#

// C# Program to find weighted mean
// of natural numbers.
using System;

class GFG {

    // Function to calculate weighted mean.
    static float weightedMean(int []X, int []W,
                                        int n)
    {
        int sum = 0, numWeight = 0;

        for (int i = 0; i < n; i++)
        {
            numWeight = numWeight + X[i] * W[i];
            sum = sum + W[i];
        }

        return (float)(numWeight) / sum;
    }

    // Driver program to test the function.
    public static void Main()
    {

        // Take num array and corresponding
        // weight array and initialize it.
        int []X = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};
        int []W = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10};

        // Calculate the size of array.
        int n = X.Length;
        int m = W.Length;

        // Check the size of both array is
        // equal or not.
        if (n == m)
            Console.WriteLine(weightedMean(X, W, n));
        else
            Console.WriteLine("-1" );
    }
}

// This code is contributed by vt_m.

PHP

<?php
// Program to find weighted mean of
// natural numbers.

// Function to calculate
// weighted mean.
function weightedMean($X, $W, $n)
{
    $sum = 0; $numWeight = 0;

    for ($i = 0; $i < $n; $i++)
    {
        $numWeight = $numWeight +
                     $X[$i] * $W[$i];
        $sum = $sum + $W[$i];
    }

    return (float)($numWeight / $sum);
}

// Driver Code

// Take num array and corresponding weight
// array and initialize it.
$X = array(1, 2, 3, 4, 5, 6, 7, 8, 9, 10);
$W = array(1, 2, 3, 4, 5, 6, 7, 8, 9, 10);

// Calculate the size of array.
$n = sizeof($X);
$m = sizeof($W);

// Check the size of both
// array is equal or not.
if ($n == $m)
    echo(weightedMean($X, $W, $n));
else
    echo("-1");

// This code is contributed by Ajit.
?>

Javascript

<script>

// Javascript program to find weighted mean
// of natural numbers.

// Function to calculate weighted mean.
function weightedMean(X, W, n)
{
    let sum = 0, numWeight = 0;

    for(let i = 0; i < n; i++)
    {
        numWeight = numWeight + X[i] * W[i];
        sum = sum + W[i];
    }

    return (numWeight) / sum;
}

// Driver code

// Take num array and corresponding
// weight array and initialize it.
let X = [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ];
let W = [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ];

// Calculate the size of array.
let n = X.length;
let m = W.length;

// Check the size of both array is
// equal or not.
if (n == m)
    document.write(weightedMean(X, W, n));
else
    document.write("-1" );

// This code is contributed by susmitakundugoaldanga

</script>

Output

7

Time Complexity: O(n)

Auxiliary Space: O(1)

Second method – to compute the weighted mean of first n natural numbers. It is the formula to compute the weighted mean of first n natural numbers. In this method, we have given first n natural number and their weight are also be the natural numbers. Then we generate the formula

Weighted Mean 
= (W[0] * X[0] + W[1] * X[1] + W[2] * X[2] + . . . +
      W[n-1] * X[n-1]) / (W[0] + W[1] + W[2] + . . . + W[n-1])
= (1 * 1 + 2 * 2 + 3 * 3 + . . . + n * n) / (1 + 2 + 3 + . . . + n)
= (n * (n + 1) * (2 * n + 1) / 6) / (n * (n + 1) / 2)

Weighted Mean = (2 * n + 1) / 3
 
Example: Weighted mean of first 10 natural numbers 
n = 10
Weighted mean 
= (2 * 10 + 1) / 3 = 21 / 3 = 7 

Implementation:

C++

// Program to find weighted mean of first
// n natural numbers using formula.
#include<bits/stdc++.h>
using namespace std;

// Returns weighted mean assuming for numbers
// {1, 2, ..n} and weights {1, 2, .. n}
int weightedMean(int n)
{
    return (2 * n + 1)/3;
}

// Driver program to test the function.
int main()
{
    int n = 10;
    cout << weightedMean(n);
    return 0;
}

Java

// Program to find weighted mean of first
// n natural numbers using formula.
import java.io.*;

public class GFG {

    // Returns weighted mean assuming for numbers
    // {1, 2, ..n} and weights {1, 2, .. n}
    static int weightedMean(int n)
    {
        return (2 * n + 1)/3;
    }

    // Driver program to test the function.

    static public void main (String[] args)
    {
        int n = 10;

        System.out.println(weightedMean(n));

    }
}

// This code is contributed by vt_m.

Python3

# Program to find weighted mean of first
# n natural numbers using formula.

# Returns weighted mean assuming for numbers
# 1, 2, ..n and weights 1, 2, .. n
def weightedMean(n):

    return (2 * n + 1) / 3

# Driver program to test the function.
n = 10
print(int(weightedMean(n)))
# This code is contributed by smita

C#

// Program to find weighted mean of first
// n natural numbers using formula.
using System;

public class GFG {

    // Returns weighted mean assuming for numbers
    // {1, 2, ..n} and weights {1, 2, .. n}
    static int weightedMean(int n)
    {
        return (2 * n + 1) / 3;
    }

    // Driver program to test the function.

    static public void Main ()
    {
        int n = 10;

        Console.WriteLine(weightedMean(n));
    }
}

// This code is contributed by vt_m.

PHP

<?php
// Program to find weighted mean of first
// n natural numbers using formula.

// Returns weighted mean
// assuming for numbers
// {1, 2, ..n} and
// weights {1, 2, .. n}
function weightedMean($n)
{
    return (2 * $n + 1) / 3;
}

// Driver Code
$n = 10;
echo(weightedMean($n));

// This code is contributed by Ajit.
?>

Javascript

<script>
    // Program to find weighted mean of first
    // n natural numbers using formula.

    // Returns weighted mean assuming for numbers
    // {1, 2, ..n} and weights {1, 2, .. n}
    function weightedMean(n)
    {
        return parseInt((2 * n + 1) / 3, 10);
    }

    let n = 10;

      document.write(weightedMean(n));

</script>

Output

7

Time complexity: O(1) as it is performing constant operations

Auxiliary space: O(1)

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