Mean and Median of a matrix

Given a sorted matrix of size n*n. Calculate the mean and median of the matrix .

Examples:

Input : 1 2 3
        4 5 6
        7 8 9
Output :Mean: 5
        Median: 5
Input : 1 1 1
        2 2 2
        4 4 4
Output :Mean: 2
        Median: 2

Mean of matrix is = 
   (sum of all elements of matrix)/
   (total elements of matrix)
Note that this definition doesn't require
matrix to be sorted and works for all
matrices.
Median of a sorted matrix is calculated as:
1. When n is odd
    median is mat[n/2][n/2]
2. When n is even, median is average
   of middle two elements.
   Middle two elements can be found at indexes
   a[(n-2)/2][n-1] and a[n/2][0]

If given matrix is unsorted, we can find its median by first sorting the matrix.

Implementation:

C++

// CPP program to find mean and median
// of sorted square matrix.
#include <bits/stdc++.h>
using namespace std;

const int N = 4;

// Returns mean of a given matrix of
// size n x n.
double findMean(int a[][N])
{
    int sum = 0;

    // total sum calculation of matrix
    for (int i=0; i<N; i++)
       for (int j=0; j<N; j++)
          sum += a[i][j];

    return (double)sum/(N*N);
}

// Function for calculating median
double findMedian(int a[][N])
{
    if (N % 2 != 0)
       return a[N/2][N/2];

    if (N%2 == 0)
       return (a[(N-2)/2][N-1] +
                       a[N/2][0])/2.0;
}

// Driver program
int main()
{
    int a[N][N]= {{1, 2, 3, 4},
                   {5, 6, 7, 8},
                   {9, 10, 11, 12},
                   {13, 14, 15, 16}};
    cout << "Mean : " << findMean(a) << endl
         << "Median : "<< findMedian(a) << endl;
    return 0;
}

// C program to find mean and median
// of sorted square matrix.
#include <stdio.h>

#define N 4
// Returns mean of a given matrix of
// size n x n.
double findMean(int a[][N])
{
    int sum = 0;

    // total sum calculation of matrix
    for (int i=0; i<N; i++)
       for (int j=0; j<N; j++)
          sum += a[i][j];

    return (double)sum/(N*N);
}

// Function for calculating median
double findMedian(int a[][N])
{
    if (N % 2 != 0)
       return a[N/2][N/2];

    if (N%2 == 0)
       return (a[(N-2)/2][N-1] +
                       a[N/2][0])/2.0;
}

// Driver program
int main()
{
    int a[N][N]= {{1, 2, 3, 4},
                   {5, 6, 7, 8},
                   {9, 10, 11, 12},
                   {13, 14, 15, 16}};
    printf("Mean : %f\n",findMean(a));
    printf("Median : %f\n",findMedian(a));
    return 0;
}

// This code is contributed by kothavvsaakash.

Java

// Java program to find mean and median
// of sorted square matrix.
import java.io.*;

class GFG
{
    
// Returns mean of a given 
// matrix of size n x n.
static double findMean(int a[][], 
                    int n)
{
    int sum = 0;
    int N=n;

    // total sum calculation of matrix
    for (int i = 0; i < N; i++)
    for (int j = 0; j < N; j++)
        sum += a[i][j];

    return (double)sum / (N * N);
}

// Function for calculating median
static double findMedian(int a[][], int n)
{ 
    int N = n;
    
    if (N % 2 != 0)
    return a[N / 2][N / 2];

    if (N % 2 == 0)
    return (a[(N - 2) / 2][ N - 1] + 
            a[ N / 2][0]) / (2.0);
    return 0;
}

    // Driver Code
    public static void main (String[] args)
    {
        int a[][]= {{1, 2, 3, 4},
                    {5, 6, 7, 8},
                    {9, 10, 11, 12},
                    {13, 14, 15, 16}};
            
        int n = a.length;
        System.out.println("Mean   : " + 
                            findMean(a, n));
        System.out.println("Median : " + 
                            findMedian(a, n));
    }
        
        
}

// This code is contributed by KRV.

Python3

# Python3 program to find mean and median
# of sorted square matrix.
N = 4

# Returns mean of a given matrix of
# size n x n.
def findMean(a):
    
    summ = 0
    
    # total sum calculation of matrix
    for i in range(N):
        for j in range(N):
            summ += a[i][j]
    
    return summ/(N*N)

# Function for calculating median
def findMedian(a):
    if (N % 2 != 0):
        return a[N//2][N//2]
    if (N % 2 == 0):
        return (a[(N - 2)//2][N - 1] + a[N//2][0])/2

# Driver program
a = [[1, 2, 3, 4],[5, 6, 7, 8],
    [9, 10, 11, 12],[13, 14, 15, 16]]
print("Mean :", findMean(a))
print("Median :",findMedian(a))

# This code is contributed by shubhamsingh10

// C# program to find mean and median
// of sorted square matrix.
using System;

class GFG {
    
    // Returns mean of a given 
    // matrix of size n x n.
    static double findMean(int [,]a, int n)
    {
        int sum = 0;
        int N = n;
    
        // total sum calculation of matrix
        for (int i = 0; i < N; i++)
            for (int j = 0; j < N; j++)
                sum += a[i,j];
    
        return (double)sum / (N * N);
    }
    
    // Function for calculating median
    static double findMedian(int [,]a, int n)
    { 
        int N = n;
        
        if (N % 2 != 0)
        return a[N / 2,N / 2];
    
        if (N % 2 == 0)
        return ( a[(N - 2) / 2, (N - 1)] +
                     a[ N / 2, 0] ) / (2.0);
        
        return 0;
    }

    // Driver Code
    public static void Main ()
    {
        int [,]a= { { 1,  2,  3,  4},
                    { 5,  6,  7,  8},
                    { 9, 10, 11, 12},
                    {13, 14, 15, 16} };
            
        int n = a.GetLength(0);
        
        Console.WriteLine("Mean : " + 
                            findMean(a, n));
                            
        Console.WriteLine("Median : " + 
                            findMedian(a, n));
    }
        
}

// This code is contributed by Sam007.

JavaScript

<script>

// Javascriptprogram to find mean and median
// of sorted square matrix.

// Returns mean of a given 
// matrix of size n x n.
function findMean(a, n)
{
    var sum = 0;
    var N = n;

    // Total sum calculation of matrix
    for(var i = 0; i < N; i++)
        for(var j = 0; j < N; j++)
            sum += a[i][j];

    return sum / (N * N);
}

// Function for calculating median
function findMedian(a, n)
{ 
    var N = n;
    
    if (N % 2 != 0)
        return a[N / 2][N / 2];

    if (N % 2 == 0)
        return (a[(N - 2) / 2][ N - 1] + 
                a[N / 2][0]) / (2.0);
    return 0;
}

// Driver Code
var a = [ [ 1, 2, 3, 4 ],
          [ 5, 6, 7, 8 ],
          [ 9, 10, 11, 12 ],
          [ 13, 14, 15, 16 ] ];
            
var n = a.length;
document.write("Mean   : " + 
               findMean(a, n) + "<br>");
document.write("Median : " + 
               findMedian(a, n) + "<br>");

// This code is contributed by Kirti

</script>

PHP

<?php
// PHP program to find 
// mean and median
// of sorted square 
// matrix.

$N = 4;

// Returns mean of 
// a given matrix of
// size n x n.
function findMean($a)
{ 
    global $N;
    $sum = 0;

    // total sum calculation
    // of matrix
    for ($i = 0; $i < $N; $i++)
    for ($j = 0; $j < $N; $j++)
        $sum += $a[$i][$j];

    return (double)$sum / ($N * $N);
}

// Function for calculating median
function findMedian($a)
{
    global $N;
    if ($N % 2 != 0)
    return $a[$N / 2][$N / 2];

    if ($N % 2 == 0)
    return ($a[($N - 2) / 2][$N - 1] + 
                 $a[$N / 2][0]) / 2.0;
}

    // Driver Code
    $a= array(array(1, 2, 3, 4),
              array(5, 6, 7, 8),
              array(9, 10, 11, 12),
              array(13, 14, 15, 16));
        echo "Mean : " , findMean($a),"\n",
             "Median : ", findMedian($a);
    
// This code is contributed by vt_m.
?>

Output

Mean : 8.5
Median : 8.5

Time complexity: O(N²) as using two for loops
Auxiliary Space: O(1)

METHOD 2:Using functions

APPROACH:

This Python program calculates the mean and median of a given matrix using functions. The program first defines two functions - mean() and median(), which take the matrix as an argument and return the calculated mean and median values, respectively. It then creates a 3x3 matrix and calls these functions to calculate the mean and median of the matrix. Finally, the program prints out the calculated mean and median values.

ALGORITHM:

Define the mean() function that takes the matrix as an argument.
- Calculate the total sum of all the values in the matrix.
- Calculate the number of values in the matrix.
- Divide the total sum by the number of values to get the mean.
- Return the mean value.
Define the median() function that takes the matrix as an argument.
Flatten the matrix into a 1D list.
Sort the list in ascending order.
Calculate the length of the list.
If the length of the list is even, calculate the average of the middle two values.
If the length of the list is odd, return the middle value.
Return the median value.

C++

// C++ Program for the above approach
#include <bits/stdc++.h>
using namespace std;

// function to find out mean value
double mean(vector<vector<int>>& matrix) {
    int total = 0;
    int count = matrix.size() * matrix[0].size();
    
    for (const auto& row : matrix) {
        for (int val : row) {
            total += val;
        }
    }
    
    return static_cast<double>(total) / count;
}

// Function to find out the media value
double median(vector<vector<int>>& matrix) {
    vector<int> flatten;
    
    for (const auto& row : matrix) {
        for (int val : row) {
            flatten.push_back(val);
        }
    }
    
      // sorting the flatten array
    sort(flatten.begin(), flatten.end());
    int n = flatten.size();
    
    if (n % 2 == 0) {
        return (static_cast<double>(flatten[n/2]) + flatten[n/2-1]) / 2;
    } else {
        return flatten[n/2];
    }
}

// Driver Program to test above functions
int main() {
      // Given Matrix
    vector<vector<int>> matrix = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
    
    double mean_value = mean(matrix);
    double median_value = median(matrix);
    
    cout << "Mean: " << mean_value << endl;
    cout << "Median: " << median_value << endl;
    
    return 0;
}

// THIS CODE IS CONTRIBUTED BY KIRTI AGARWAL

Java

import java.util.ArrayList;
import java.util.Collections;
import java.util.List;

public class Main {

    // function to find out mean value
    static double mean(List<List<Integer> > matrix)
    {
        int total = 0;
        int count = matrix.size() * matrix.get(0).size();

        for (List<Integer> row : matrix) {
            for (int val : row) {
                total += val;
            }
        }

        return (double)total / count;
    }

    // Function to find out the median value
    static double median(List<List<Integer> > matrix)
    {
        List<Integer> flatten = new ArrayList<>();

        for (List<Integer> row : matrix) {
            for (int val : row) {
                flatten.add(val);
            }
        }

        // sorting the flatten array
        Collections.sort(flatten);
        int n = flatten.size();

        if (n % 2 == 0) {
            return ((double)flatten.get(n / 2)
                    + flatten.get(n / 2 - 1))
                / 2;
        }
        else {
            return flatten.get(n / 2);
        }
    }

    // Driver Program to test above functions
    public static void main(String[] args)
    {
        // Given Matrix
        List<List<Integer> > matrix = new ArrayList<>();
        matrix.add(new ArrayList<>(List.of(1, 2, 3)));
        matrix.add(new ArrayList<>(List.of(4, 5, 6)));
        matrix.add(new ArrayList<>(List.of(7, 8, 9)));

        double mean_value = mean(matrix);
        double median_value = median(matrix);

        System.out.println("Mean: " + mean_value);
        System.out.println("Median: " + median_value);
    }
}
// This code is contributed by akshitaguprzj3

Python3

def mean(matrix):
    total = sum(val for row in matrix for val in row)
    count = len(matrix) * len(matrix[0])
    return total / count

def median(matrix):
    flatten = [val for row in matrix for val in row]
    flatten.sort()
    n = len(flatten)
    if n % 2 == 0:
        return (flatten[n//2] + flatten[n//2-1]) / 2
    else:
        return flatten[n//2]

# Create a 3x3 matrix
matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]

# Calculate mean and median
mean_value = mean(matrix)
median_value = median(matrix)

# Print the results
print("Mean:", mean_value)
print("Median:", median_value)

using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    // Function to find out mean value
    static double Mean(List<List<int>> matrix)
    {
        int total = 0;
        int count = matrix.Count * matrix[0].Count;

        foreach (var row in matrix)
        {
            foreach (int val in row)
            {
                total += val;
            }
        }

        return (double)total / count;
    }

    // Function to find out the median value
    static double Median(List<List<int>> matrix)
    {
        List<int> flatten = new List<int>();

        foreach (var row in matrix)
        {
            foreach (int val in row)
            {
                flatten.Add(val);
            }
        }

        // Sorting the flatten list
        flatten.Sort();
        int n = flatten.Count;

        if (n % 2 == 0)
        {
            return ((double)flatten[n / 2] + flatten[n / 2 - 1]) / 2;
        }
        else
        {
            return flatten[n / 2];
        }
    }

    // Driver Program to test above functions
    static void Main(string[] args)
    {
        // Given Matrix
        List<List<int>> matrix = new List<List<int>>
        {
            new List<int> {1, 2, 3},
            new List<int> {4, 5, 6},
            new List<int> {7, 8, 9}
        };

        double meanValue = Mean(matrix);
        double medianValue = Median(matrix);

        Console.WriteLine($"Mean: {meanValue}");
        Console.WriteLine($"Median: {medianValue}");
    }
}
// This code is contributed by akshitaguprzj3

JavaScript

// Function to calculate the mean of a matrix
function mean(matrix) {
    let total = matrix.flat().reduce((sum, val) => sum + val, 0);
    let count = matrix.length * matrix[0].length;
    return total / count;
}

// Function to calculate the median of a matrix
function median(matrix) {
    let flatten = matrix.flat().sort((a, b) => a - b);
    let n = flatten.length;
    if (n % 2 === 0) {
        return (flatten[n / 2] + flatten[n / 2 - 1]) / 2;
    } else {
        return flatten[Math.floor(n / 2)];
    }
}

// Create a 3x3 matrix
let matrix = [[1, 2, 3], [4, 5, 6], [7, 8, 9]];

// Calculate mean and median
let meanValue = mean(matrix);
let medianValue = median(matrix);

// Print the results
console.log("Mean:", meanValue);
console.log("Median:", medianValue);

// THIS CODE IS CONTRIBUTED BY KIRTI AGARWAL

Output

Mean: 5.0
Median: 5

Time Complexity: The time complexity of this program is O(nlogn) for sorting the list, where n is the total number of elements in the matrix.
Space Complexity: The space complexity of this program is O(n) for storing the flattened list, where n is the total number of elements in the matrix.

Mean and Median of a matrix

Explore