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++

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// 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;
}

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Java

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// 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.

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C#

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// 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.

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PHP

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<?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.
?>

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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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Improved By : KRV, vt_m, Sam007