iqr

Interquartile range of probability distribution

Syntax

r = iqr(pd)

Description

r = iqr(pd) returns the interquartile range of the probability distribution pd. The scalar value of r is the difference between the values of the 75th and 25th percentiles of the probability distribution.

Examples

Compute the Normal Distribution Interquartile Range

Create a standard normal distribution object with the mean, $$\mu$$, equal to 0 and the standard deviation, $$\sigma$$, equal to 1.

pd = makedist('Normal','mu',0,'sigma',1);

Compute the interquartile range of the standard normal distribution.

r = iqr(pd)

r = 
1.3490

The returned value is the difference between the 75th and the 25th percentile values for the distribution. This is equivalent to computing the difference between the inverse cumulative distribution function (icdf) values at the probabilities y equal to 0.75 and 0.25.

r2 = icdf(pd,0.75) - icdf(pd,0.25)

r2 = 
1.3490

Interquartile Range of a Fitted Distribution

Load the sample data. Create a vector containing the first column of students’ exam grade data.

load examgrades;
x = grades(:,1);

Create a normal distribution object by fitting it to the data.

pd = fitdist(x,'Normal')

pd = 
  NormalDistribution

  Normal distribution
       mu = 75.0083   [73.4321, 76.5846]
    sigma =  8.7202   [7.7391, 9.98843]

Compute the interquartile range of the fitted distribution.

r = iqr(pd)

r = 
11.7634

The returned result indicates that the difference between the 75th and 25th percentile of the students’ grades is 11.7634.

Use icdf to determine the 75th and 25th percentiles of the students’ grades.

y = icdf(pd,[0.25,0.75])

y = 1×2

   69.1266   80.8900

Calculate the difference between the 75th and 25th percentiles. This yields the same result as iqr.

y(2)-y(1)

ans = 
11.7634

Use boxplot to visualize the interquartile range.

boxplot(x)

The top line of the box shows the 75th percentile, and the bottom line shows the 25th percentile. The center line shows the median, which is the 50th percentile.

Input Arguments

pd — Probability distribution

probability distribution object

Probability distribution, specified as one of the probability distribution objects in the following table.

Distribution Object	Function or App Used to Create Probability Distribution Object
BetaDistribution	makedist, fitdist, Distribution Fitter
BinomialDistribution	makedist, fitdist, Distribution Fitter
BirnbaumSaundersDistribution	makedist, fitdist, Distribution Fitter
BurrDistribution	makedist, fitdist, Distribution Fitter
ExponentialDistribution	makedist, fitdist, Distribution Fitter
ExtremeValueDistribution	makedist, fitdist, Distribution Fitter
GammaDistribution	makedist, fitdist, Distribution Fitter
GeneralizedExtremeValueDistribution	makedist, fitdist, Distribution Fitter
GeneralizedParetoDistribution	makedist, fitdist, Distribution Fitter
HalfNormalDistribution	makedist, fitdist, Distribution Fitter
InverseGaussianDistribution	makedist, fitdist, Distribution Fitter
KernelDistribution	fitdist, Distribution Fitter
LogisticDistribution	makedist, fitdist, Distribution Fitter
LoglogisticDistribution	makedist, fitdist, Distribution Fitter
LognormalDistribution	makedist, fitdist, Distribution Fitter
LoguniformDistribution	makedist
MultinomialDistribution	makedist
NakagamiDistribution	makedist, fitdist, Distribution Fitter
NegativeBinomialDistribution	makedist, fitdist, Distribution Fitter
NormalDistribution	makedist, fitdist, Distribution Fitter
PiecewiseLinearDistribution	makedist
PoissonDistribution	makedist, fitdist, Distribution Fitter
RayleighDistribution	makedist, fitdist, Distribution Fitter
RicianDistribution	makedist, fitdist, Distribution Fitter
StableDistribution	makedist, fitdist, Distribution Fitter
tLocationScaleDistribution	makedist, fitdist, Distribution Fitter
TriangularDistribution	makedist
UniformDistribution	makedist
WeibullDistribution	makedist, fitdist, Distribution Fitter

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

• The input argument pd can be a fitted probability distribution object for beta, exponential, extreme value, lognormal, normal, and Weibull distributions. Create pd by fitting a probability distribution to sample data from the fitdist function. For an example, see Code Generation for Probability Distribution Objects.

For more information on code generation, see Introduction to Code Generation and General Code Generation Workflow.

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).

Version History

Introduced in R2013a