# mean

Average or mean value of array

## Description

example

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 dimension becomes 1 while the sizes of all other dimensions remain the same.

example

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

example

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.

example

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.

example

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'.

example

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

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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

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

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

A = gallery('integerdata',10,[4,2,3],1);
M = mean(A,2)
M =
M(:,:,1) =

9.5000
6.5000
9.5000
6.0000

M(:,:,2) =

1.5000
4.0000
7.5000
7.5000

M(:,:,3) =

7.0000
2.5000
4.0000
5.5000

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

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'

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

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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

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 mean(A,1) returns a row vector containing the mean of the elements in each column.

• If dim = 2, then mean(A,2) returns a column vector containing the mean of the elements in each row.

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

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

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.

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

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

outtypeOutput 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

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

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### Mean

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

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