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

A simple solution to solve weighed mean.

// 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;
}

Output –

7

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
// 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;
}

Output –

7

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source and credits.
source and credits: http://www.geeksforgeeks.org
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rakesh

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