median

Median value of array

Syntax

M = median(A)

M = median(A,'all')

M = median(A,dim)

M = median(A,vecdim)

M = median(___,nanflag)

Description

M = median(A) returns the median value of A.

• If A is a vector, then median(A) returns the median value of A.

• If A is a nonempty matrix, then median(A) treats the columns of A as vectors and returns a row vector of median values.

• If A is an empty 0-by-0 matrix, median(A) returns NaN.

• If A is a multidimensional array, then median(A) treats the values along the first array dimension whose size does not equal 1 as vectors. The size of this dimension becomes 1 while the sizes of all other dimensions remain the same.

median computes natively in the numeric class of A, such that class(M) = class(A).

M = median(A,'all') computes the median over all elements of A. This syntax is valid for MATLAB^® versions R2018b and later.

M = median(A,dim) returns the median of elements along dimension dim. For example, if A is a matrix, then median(A,2) is a column vector containing the median value of each row.

M = median(A,vecdim) computes the median based on the dimensions specified in the vector vecdim. For example, if A is a matrix, then median(A,[1 2]) is the median over all elements in A, since every element of a matrix is contained in the array slice defined by dimensions 1 and 2.

M = median(___,nanflag) optionally specifies whether to include or omit NaN values in the median calculation for any of the previous syntaxes. For example, median(A,'omitnan') ignores all NaN values in A.

Examples

Median of Matrix Columns

Define a 4-by-3 matrix.

A = [0 1 1; 2 3 2; 1 3 2; 4 2 2]

A = 4×3

     0     1     1
     2     3     2
     1     3     2
     4     2     2

Find the median value of each column.

M = median(A)

M = 1×3

    1.5000    2.5000    2.0000

For each column, the median value is the mean of the middle two numbers in sorted order.

Median of Matrix Rows

Define a 2-by-3 matrix.

A = [0 1 1; 2 3 2]

A = 2×3

     0     1     1
     2     3     2

Find the median value of each row.

M = median(A,2)

M = 2×1

     1
     2

For each row, the median value is the middle number in sorted order.

Median of 3-D Array

Create a 1-by-3-by-4 array of integers between 1 and 10.

rng('default')
A = randi(10,[1,3,4])

A = 
A(:,:,1) =

     9    10     2


A(:,:,2) =

    10     7     1


A(:,:,3) =

     3     6    10


A(:,:,4) =

    10     2    10

Find the median values of this 3-D array along the second dimension.

M = median(A)

M = 
M(:,:,1) =

     9


M(:,:,2) =

     7


M(:,:,3) =

     6


M(:,:,4) =

    10

This operation produces a 1-by-1-by-4 array by computing the median of the three values along the second dimension. The size of the second dimension is reduced to 1.

Compute the median along the first dimension of A.

M = median(A,1);
isequal(A,M)

ans = logical
   1

This command returns the same array as A because the size of the first dimension is 1.

Median of Array Page

Create a 3-D array and compute the median over each page of data (rows and columns).

A(:,:,1) = [2 4; -2 1];
A(:,:,2) = [6 2; -5 3];
A(:,:,3) = [4 4; 7 -3];
M1 = median(A,[1 2])

M1 = 
M1(:,:,1) =

    1.5000


M1(:,:,2) =

    2.5000


M1(:,:,3) =

     4

Starting in R2018b, to compute the median over all dimensions of an array, you can either specify each dimension in the vector dimension argument, or use the 'all' option.

M2 = median(A,[1 2 3])

M2 = 2.5000

Mall = median(A,'all')

Mall = 2.5000

Median of 8-Bit Integer Array

Define a 1-by-4 vector of 8-bit integers.

A = int8(1:4)

A = 1x4 int8 row vector

   1   2   3   4

Compute the median value.

M = median(A),

M = int8
    3

class(M)

ans = 
'int8'

M is the mean of the middle two numbers in sorted order returned as an 8-bit integer.

Median Excluding NaN

Create a vector and compute its median, excluding NaN values.

A = [1.77 -0.005 3.98 -2.95 NaN 0.34 NaN 0.19];
M = median(A,'omitnan')

M = 0.2650

Input Arguments

A — Input array

vector | matrix | multidimensional array

Input array, specified as a vector, matrix, or multidimensional array. A can be a numeric array, ordinal categorical array, datetime array, or duration array.

dim — Dimension to operate along

positive integer scalar

Dimension to operate along, specified as a positive integer scalar. If you do not specify the dimension, then the default is the first array dimension of size greater than 1.

Dimension dim indicates the dimension whose length reduces to 1. The size(M,dim) is 1, while the sizes of all other dimensions remain the same.

Consider an m-by-n input matrix, A:

• median(A,1) computes the median of the elements in each column of A and returns a 1-by-n row vector.

  

• median(A,2) computes the median of the elements in each row of A and returns an m-by-1 column vector.

  

median returns A when dim is greater than ndims(A).

vecdim — Vector of dimensions

vector of positive integers

Vector of dimensions, specified as a vector of positive integers. Each element represents a dimension of the input array. The lengths of the output in the specified operating dimensions are 1, while the others remain the same.

Consider a 2-by-3-by-3 input array, A. Then median(A,[1 2]) returns a 1-by-1-by-3 array whose elements are the medians of each page of A.

nanflag — NaN condition

'includenan' (default) | 'omitnan'

NaN condition, specified as one of these values:

• 'includenan' — the median of input containing NaN values is also NaN.

• 'omitnan' — all NaN values appearing in the input are ignored. Note: the NaN flags are not set to 0.

You also can specify additional values for some data types.

• 'includeundefined' and 'omitundefined' — categorical input

• 'includenat' and 'omitnat' — datetime input

Algorithms

For ordinal categorical arrays, MATLAB interprets the median of an even number of elements as follows:

If the number of categories between the middle two values is ...	Then the median is ...
zero (values are from consecutive categories)	larger of the two middle values
an odd number	value from category occurring midway between the two middle values
an even number	value from larger of the two categories occurring midway between the two middle values

Extended Capabilities

Tall Arrays

Calculate with arrays that have more rows than fit in memory.

Usage notes and limitations:

Input A must be a column vector to compute median in the first dimension.

For more information, see Tall Arrays.

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• If specified, dim must be a constant.

• Variable-Sizing Restrictions for Code Generation of Toolbox Functions (MATLAB Coder)

• Code Generation for Complex Data with Zero-Valued Imaginary Parts (MATLAB Coder).

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Distributed Arrays

Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

This function fully supports distributed arrays. For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a