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.

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; 
} 

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. 

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. 

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

This article is contributed by Himanshu Ranjan. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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