median

Median value of array

Description

example

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).

example

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

example

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.

example

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.

example

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

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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.

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.

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.

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

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.

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

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

Dimension to operate along, specified as a positive integer scalar. If no value is specified, then the default is the first array dimension whose size does not equal 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 a two-dimensional input array, A.

• If dim = 1, then median(A,1) returns a row vector containing the median of the elements in each column. • If dim = 2, then median(A,2) returns a column vector containing the median of the elements in each row. median returns A when dim is greater than ndims(A).

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. Data Types: double | single | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

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 numbervalue from category occurring midway between the two middle values
an even numbervalue from larger of the two categories occurring midway between the two middle values