Mean and Median of a matrix - GeeksforGeeks

19 Apr, 2021
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++
Java
Python3
C#
PHP
Javascript
// 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 mediandouble 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 programint 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 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 medianstatic 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 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 mediandef 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 programa = [[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.
<?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 * $N);} // Function for calculating medianfunction findMedian($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.?>
<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 medianfunction 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 Codevar 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>
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.Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. 
KRV
vt_m
Sam007
SHUBHAMSINGH10
Kirti_Mangal
maths-mean
median-finding
Order-Statistics
statistical-algorithms
Matrix
Matrix
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