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

// 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#

// 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)

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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 3×3 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)

C#

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.