# 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

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

collapse all

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

collapse all

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