mean

Average or mean value of array

Syntax

M = mean(A)

M = mean(A,'all')

M = mean(A,dim)

M = mean(A,vecdim)

M = mean(___,outtype)

M = mean(___,nanflag)

Description

M = mean(A) returns the mean of the elements of A along the first array dimension whose size does not equal 1.

• If A is a vector, then mean(A) returns the mean of the elements.

• If A is a matrix, then mean(A) returns a row vector containing the mean of each column.

• If A is a multidimensional array, then mean(A) operates along the first array dimension whose size does not equal 1, treating the elements as vectors. This size of this dimension becomes 1 while the sizes of all other dimensions remain the same as A.

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

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

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

M = mean(___,outtype) returns the mean with a specified data type, using any of the input arguments in the previous syntaxes. outtype can be 'default', 'double', or 'native'.

M = mean(___,nanflag) specifies whether to include or omit NaN values from the calculation for any of the previous syntaxes. mean(A,'includenan') includes all NaN values in the calculation while mean(A,'omitnan') ignores them.

Examples

Mean of Matrix Columns

Create a matrix and compute the mean of each column.

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

M = mean(A)

M = 1×3

    1.7500    2.2500    1.7500

Mean of Matrix Rows

Create a matrix and compute the mean of each row.

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

A = 4×3

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

M = mean(A,2)

M = 4×1

    0.6667
    2.3333
    1.3333
    2.0000

Mean of 3-D Array

Create a 4-by-2-by-3 array of integers between 1 and 10 and compute the mean values along the second dimension.

rng('default')
A = randi(10,[4,2,3]);
M = mean(A,2)

M = 
M(:,:,1) =

    8.0000
    5.5000
    2.5000
    8.0000


M(:,:,2) =

   10.0000
    7.5000
    5.5000
    6.0000


M(:,:,3) =

    6.0000
    5.5000
    8.5000
   10.0000

Mean of Array Page

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

A(:,:,1) = [2 4; -2 1];
A(:,:,2) = [9 13; -5 7];
A(:,:,3) = [4 4; 8 -3];
M1 = mean(A,[1 2])

M1 = 
M1(:,:,1) =

    1.2500


M1(:,:,2) =

     6


M1(:,:,3) =

    3.2500

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

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

M2 = 3.5000

Mall = mean(A,'all')

Mall = 3.5000

Mean of Single-Precision Array

Create a single-precision vector of ones and compute its single-precision mean.

A = single(ones(10,1));
M = mean(A,'native')

M = single
    1

The result is also in single precision.

class(M)

ans = 
'single'

Mean Excluding NaN

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

A = [1 0 0 1 NaN 1 NaN 0];
M = mean(A,'omitnan')

M = 0.5000

If you do not specify 'omitnan', then mean(A) returns NaN.

Input Arguments

A — Input array

vector | matrix | multidimensional array

Input array, specified as a vector, matrix, or multidimensional array.

• If A is a scalar, then mean(A) returns A.

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

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | logical | char | datetime | duration

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:

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

  

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

  

mean returns A when dim is greater than ndims(A) or when size(A,dim) is 1.

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 mean(A,[1 2]) returns a 1-by-1-by-3 array whose elements are the means over each page of A.

outtype — Output data type

'default' (default) | 'double' | 'native'

Output data type, specified as 'default', 'double', or 'native'. These options also specify the data type in which the operation is performed.

outtype	Output data type
'default'	double, unless the input data type is single, duration, or datetime, in which case, the output is 'native'
'double'	double, unless the data type is duration or datetime, in which case, 'double' is not supported
'native'	Same data type as the input, unless Input data type is logical, in which case, the output is double Input data type is char, in which case, 'native'is not supported

Data Types: char

nanflag — NaN condition

'includenan' (default) | 'omitnan'

NaN condition, specified as one of these values:

• 'includenan' — Include NaN values when computing the mean, resulting in NaN.

• 'omitnan' — Ignore all NaN values in the input.

For datetime arrays, you can also use 'omitnat' or 'includenat' to omit and include NaT values, respectively.

Data Types: char

More About

Mean

For a random variable vector A made up of N scalar observations, the mean is defined as

$$\mu =\frac{1}{N}{\displaystyle \sum _{i=1}^N{A}_i}.$$

Extended Capabilities

Tall Arrays

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

This function fully supports tall arrays. For more information, see Tall Arrays.

C/C++ Code Generation

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

Usage notes and limitations:

• If you specify dim, then it must be a constant.

• The outtype and nanflag options must be constant character vectors.

• Integer types do not support the 'native' output data type option.

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

GPU Code Generation

Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

Usage notes and limitations:

• If you specify dim, then it must be a constant.

• The outtype and nanflag options must be constant character vectors.

• Integer types do not support the 'native' output data type option.

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™.

Usage notes and limitations:

• The 'native' option is not supported.

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™.

Usage notes and limitations:

• The 'native' option is not supported.

For more information, see Run MATLAB Functions with Distributed Arrays (Parallel Computing Toolbox).

Version History

Introduced before R2006a