iqr

Interquartile range of data set

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Syntax

r = iqr(A)

r = iqr(A,"all")

r = iqr(A,dim)

r = iqr(A,vecdim)

Description

example

r = iqr(A) returns the interquartile range values of elements in input data A.

If A is a vector, then r is the difference between the 75th and the 25th percentiles of the data contained in A.
If A is a matrix, then r is a row vector containing the difference between the 75th and the 25th percentiles of the sample data in each column of A.
If A is a multidimensional array, then r contains the interquartile range values computed along the first array dimension of size greater than 1. The size of this dimension is 1 while the sizes of all other dimensions remain the same as the input data.

example

r = iqr(A,"all") returns the interquartile range values of all the elements in A.

example

r = iqr(A,dim) operates along the dimension dim. For example, if A is a matrix, then iqr(A,2) operates on the elements in each row.

example

r = iqr(A,vecdim) operates along the dimensions specified in the vector vecdim. For example, if A is a matrix, then iqr(A,[1 2]) operates on all the elements of A because every element of a matrix is contained in the array slice defined by dimensions 1 and 2.

Examples

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Interquartile Range of Matrix Columns or Rows

Open Live Script

Generate a 4-by-4 matrix of normally distributed random data.

rng default % for reproducibility
A = randn(4,4)

A = 4×4

    0.5377    0.3188    3.5784    0.7254
    1.8339   -1.3077    2.7694   -0.0631
   -2.2588   -0.4336   -1.3499    0.7147
    0.8622    0.3426    3.0349   -0.2050

Compute the interquartile range for each column of data.

r = iqr(A)

r = 1×4

    2.2086    1.2013    2.5969    0.8541

Compute the interquartile range for each row of data.

r2 = iqr(A,2)

Interquartile Range of Multidimensional Array

Open Live Script

Compute the interquartile range of a multidimensional array over multiple dimensions by specifying the "all" or vecdim input.

Create a 3-by-4-by-2 array.

A = reshape(1:24,[3 4 2])

A = 
A(:,:,1) =

     1     4     7    10
     2     5     8    11
     3     6     9    12


A(:,:,2) =

    13    16    19    22
    14    17    20    23
    15    18    21    24

Compute the interquartile range of all the values in A.

rall = iqr(A,"all")

rall = 12

Compute the interquartile range of each page of A. Specify the first and second dimensions as the operating dimensions along which the interquartile range is calculated.

rPage = iqr(A,[1 2])

rPage = 
rPage(:,:,1) =

     6


rPage(:,:,2) =

     6

rPage(1,1,1) is the interquartile range of all the elements in A(:,:,1).

Compute the interquartile range of the elements in each A(i,:,:) slice by specifying the second and third dimensions as the operating dimensions.

rRow = iqr(A,[2 3])

rRow(3) is the interquartile range of all the elements in A(3,:,:).

Input Arguments

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`A` — Input array
vector | matrix | multidimensional array

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

Data Types: single | double

`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.

Consider an input matrix A:

r = iqr(A,1) computes the interquartile range of the columns in A. Because 1 is the specified operating dimension, r has a number of rows equal to the number of columns in A.
r = iqr(A,2) computes the interquartile range of the rows in A. Because 2 is the specified operating dimension, r has a number of columns equal to the number of rows in A.

Dimension dim indicates the dimension of r whose length reduces to 1. The size(r,dim) is 1, while the sizes of all other dimensions of output r remain the same as the input data.

`vecdim` — Vector of dimensions to operate along
vector of positive integers

Vector of dimensions to operate along, specified as a vector of positive integers. Each element represents a dimension of the input data.

The size of the output r in the specified operating dimensions is 1. The length of r in all other dimensions remains the same as the input data.

Consider a 2-by-3-by-3 input array, A. iqr(A,[1 2]) returns a 1-by-1-by-3 array because 1 and 2 are the operating dimensions. Each page of the output array contains the interquartile range of the elements on the corresponding page of A.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

The "all" and the vecdim inputs are not supported.
The dim input argument must be a compile-time constant.
If you do not specify the dim input argument, the working (or operating) dimension can be different in the generated code. As a result, run-time errors can occur. For more details, see Automatic dimension restriction (MATLAB Coder).

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. 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

expand all

R2022b: Improved performance with small input data

The iqr function shows improved performance due to faster input parsing. The performance improvement is most significant when input parsing is a greater portion of the computation time. This situation occurs when:

The size of the input data is small.
Computation is along the default operating dimension.

For example, this code calculates the interquartile range of a 4000-element matrix. The code is about 4.67x faster than in the previous release.

function timingIqr
A = rand(400,10);
for k = 1:3e3
  r = iqr(A);
end
end

The approximate execution times are:

R2022a: 0.98 s

R2022b: 0.21 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(@timingIqr)

R2022a: Moved to MATLAB from Statistics and Machine Learning Toolbox

Previously, iqr required Statistics and Machine Learning Toolbox™.

iqr

Syntax

Description

Examples

Interquartile Range of Matrix Columns or Rows

Interquartile Range of Multidimensional Array

Input Arguments

A — Input array vector | matrix | multidimensional array

dim — Dimension to operate along positive integer scalar

vecdim — Vector of dimensions to operate along vector of positive integers

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

GPU Arrays Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed Arrays Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.

Version History

R2022b: Improved performance with small input data

R2022a: Moved to MATLAB from Statistics and Machine Learning Toolbox

See Also

WeChat

`A` — Input array
vector | matrix | multidimensional array

`dim` — Dimension to operate along
positive integer scalar

`vecdim` — Vector of dimensions to operate along
vector of positive integers

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Distributed Arrays
Partition large arrays across the combined memory of your cluster using Parallel Computing Toolbox™.