# Mean and Median of a matrix

• Difficulty Level : Easy
• Last Updated : 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```

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```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]    ```

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 ``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

## 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.`

## PHP

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## Javascript

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Output:

```Mean : 8.5
Median : 8.5```

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