How to Find the Variance of Numbers in 2D Array in C++?

Last Updated : 14 Feb, 2024

The variance of numbers is a measure of the spread of a set of values which is used to find how much the values in a dataset differ from mean or average. In this article, we will learn how to find the variance of numbers in a 2D array in C++.

Example

Input: 
myMatrix = { { 10, 20, 30 },
                        { 40, 50, 60 },
                        { 70, 80, 90 } };

Output:
Variance: 666.667

Variance in a 2D Array in C++

To find the Variance in a 2D array we need to first calculate the mean i.e. the average of all the elements in a given 2D array:

The formula for Mean:

$\text{Mean Discrete}\ \mu=E(X)=\sum P_{i}x_{i}$

Then use that mean to find the variance (σ2) using the below formula for the set of n values (x₁, x₂,…, xₙ).

Formula for Variance:

$\sigma^{2}=\sum P_{i}(x_{i} -\mu)^2$

C++ Program to Find the Variance in a 2D Array

The below example demonstrates how we can find a variance in a 2D array in C++.

C++

// C++ Program to find the variance in a 2D array 
  
#include <cmath> 
#include <iostream> 
  
using namespace std; 
  
// Function to calculate the overall mean and variance of a 
// 2D array 
double calculateVariance(int rows, int cols, 
                         int matrix[][3]) 
{ 
    double sum = 0; 
    double squaredDiff = 0; 
    int totalCount = rows * cols; 
  
    // Calculate the sum of all elements 
    for (int i = 0; i < rows; ++i) { 
        for (int j = 0; j < cols; ++j) { 
            sum += matrix[i][j]; 
        } 
    } 
  
    // Calculate the overall mean 
    double overallMean = sum / totalCount; 
  
    // Calculate the squared difference from the mean for 
    // each element 
    for (int i = 0; i < rows; ++i) { 
        for (int j = 0; j < cols; ++j) { 
            squaredDiff 
                += pow(matrix[i][j] - overallMean, 2); 
        } 
    } 
  
    // Calculate variance 
    double variance = squaredDiff / totalCount; 
  
    return variance; 
} 
  
int main() 
{ 
    const int rows = 3; 
    const int cols = 3; 
    int matrix[rows][cols] = { { 10, 20, 30 }, 
                               { 40, 50, 60 }, 
                               { 70, 80, 90 } }; 
  
    double result = calculateVariance(rows, cols, matrix); 
    cout << "Variance: " << result << endl; 
  
    return 0; 
}