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(___,missingflag)

M = mean(___,Weights=W)

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. The size of M in this dimension becomes 1, while the sizes of all other dimensions remain the same as in A.

• If A is a table or timetable, then mean(A) returns a one-row table containing the mean of each variable. (since R2023a)

M = mean(A,"all") returns the mean over all elements of A.

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

M = mean(A,vecdim) returns the mean based on the dimensions specified in the vector vecdim. For example, if A is a matrix, then mean(A,[1 2]) returns the mean of all elements in A because 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 for any of the previous syntaxes. outtype can be "default", "double", or "native".

M = mean(___,missingflag) specifies whether to include or omit missing values in A. For example, mean(A,"omitmissing") ignores all missing values when computing the mean. By default, mean includes missing values.

M = mean(___,Weights=W) specifies a weighting scheme W and returns the weighted mean. (since R2024a)

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

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 Missing Values

Create a matrix containing NaN values.

A = [1.77 -0.005 NaN -2.95; NaN 0.34 NaN 0.19]

A = 2×4

    1.7700   -0.0050       NaN   -2.9500
       NaN    0.3400       NaN    0.1900

Compute the mean values of the matrix, excluding missing values. For matrix columns that contain any NaN value, mean computes with the non-NaN elements. For matrix columns that contain all NaN values, the mean is NaN.

M = mean(A,"omitnan")

M = 1×4

    1.7700    0.1675       NaN   -1.3800

Weighted Mean

Since R2024a

Create a matrix and compute the weighted mean of the matrix according to a weighting scheme specified by W. The mean function applies the weighting scheme to each column in A.

A = [1 1; 7 9; 1 9; 1 9; 6 2];
W = [1 2 1 2 3]';
M = mean(A,Weights=W)

M = 1×2

    4.0000    5.7778

Input Arguments

A — Input data

vector | matrix | multidimensional array | table | timetable

Input data, specified as a vector, matrix, multidimensional array, table, or timetable.

• 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 | datetime | duration | table | timetable

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 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 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 data. 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 data, 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 one of the values in this table. 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, datetime, table, or timetable, in which case, the output is "native"
"double"	double, unless the data input type is duration, datetime, table, or timetable, 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 Input data type is timetable, in which case, the output is table

missingflag — Missing value condition

"includemissing" (default) | "includenan" | "includenat" | "omitmissing" | "omitnan" | "omitnat"

Missing value condition, specified as one of the values in this table.

Value	Input Data Type	Description
"includemissing"	All supported data types	Include missing values in A when computing the mean. If any element in the operating dimension is missing, then the corresponding element in M is missing.
"includenan"	double, single, duration
"includenat"	datetime
"omitmissing"	All supported data types	Ignore missing values in A, and compute the mean over fewer points. If all elements in the operating dimension are missing, then the corresponding element in M is missing.
"omitnan"	double, single, duration
"omitnat"	datetime

W — Weighting scheme

vector | matrix | multidimensional array

Since R2024a

Weighting scheme, specified as a vector, matrix, or multidimensional array. The elements of W must be nonnegative.

If you specify a weighting scheme, mean returns the weighted mean, which is useful when values in the input data have different levels of importance or the input data is skewed.

If W is a vector, it must have the same length as the operating dimension. Otherwise, W must have the same size as the input data.

If the input data A is a table or timetable, then W must be a vector.

You cannot specify this argument if you specify vecdim or "all".

Data Types: double | single

More About

Mean

For a finite-length vector A made up of N scalar observations, the mean is defined as

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

Weighted Mean

For a finite-length vector A made up of N scalar observations and weighting scheme W, the weighted mean is defined as

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

Extended Capabilities

Tall Arrays

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

The mean function supports tall arrays with the following usage notes and limitations:

• The "native" output data type option is not supported for integer types.

• The Weights name-value argument is not supported.

For more information, see Tall Arrays.

C/C++ Code Generation

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

Usage notes and limitations:

• If used, the dim, vecdim, outtype, and missingflag arguments must be constant at code generation time.

• Code generation does not support the "native" output data type option for integer data types.

• For input argument A:

  • If you do not specify a dimension, the code generator operates along the first dimension of the input array that is variable size or whose size does not equal 1. If this dimension is variable size at code generation time and is 1 at run time, a run-time error can occur. To avoid this error, specify the dimension.

  • If all dimensions of the input array are variable size at code generation time, this array cannot be empty at run time.

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 missingflag options must be constant character vectors or strings.

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

• The Weights name-value argument is not supported.

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™.

The mean function fully supports GPU arrays. To run the function on a GPU, specify the input data as a gpuArray (Parallel Computing Toolbox). 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

R2024b: Compute weighted mean for datetime data type

You can compute the weighted mean for input data having the datetime data type. Before R2024b, you could compute only the unweighted mean for this data type.

R2024a: Compute weighted mean

Compute the weighted mean by specifying the Weights parameter as the weighting scheme. You can compute the weighted mean for input data having numeric, logical, and duration data types.

R2023a: Perform calculations directly on tables and timetables

The mean function can calculate on all variables within a table or timetable without indexing to access those variables. All variables must have data types that support the calculation. For more information, see Direct Calculations on Tables and Timetables.

R2023a: Specify missing value condition

Include or omit all missing values in the input data when computing the mean by using the "includemissing" or "omitmissing" options. Previously, "includenan", "omitnan", "includenat", and "omitnat" specified a missing value condition that was specific to the data type of the input data.

R2023a: Improved performance with small group size

The mean function shows improved performance when computing over a real vector when the operating dimension is not specified. The function determines the default operating dimension more quickly in R2023a than in R2022b.

For example, this code computes the mean along the default vector dimension. The code is about 2.2x faster than in the previous release.

function timingMean
A = rand(10,1);
for i = 1:8e5
    mean(A);
end
end

The approximate execution times are:

R2022b: 0.91 s

R2023a: 0.41 s

The code was timed on a Windows^® 10, Intel^® Xeon^® CPU E5-1650 v4 @ 3.60 GHz test system using the timeit function.

timeit(@timingMean)

R2018b: Operate on multiple dimensions

Operate on multiple dimensions of the input data at a time. Specify a vector of operating dimensions, or specify the "all" option to operate on all array dimensions.