median

Median of probability distribution

Syntax

m = median(pd)

Description

m = median(pd) returns the median m for the probability distribution pd

Examples

Median 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 median of the fitted distribution.

m = median(pd)

m = 75.0083

For a symmetrical distribution such as the normal distribution, the median is equal to the mean, mu.

Median of a Skewed Distribution

Create a Weibull probability distribution object.

pd = makedist('Weibull','a',5,'b',2)

pd = 
  WeibullDistribution

  Weibull distribution
    A = 5
    B = 2

Compute the median of the distribution.

m = median(pd)

m = 4.1628

For a skewed distribution such as the Weibull distribution, the median and the mean may not be equal.

Calculate the mean of the Weibull distribution and compare it to the median.

mean = mean(pd)

mean = 4.4311

The mean of the distribution is greater than the median.

Plot the pdf to visualize the distribution.

x = [0:.1:15];
pdf = pdf(pd,x);
plot(x,pdf)

Input Arguments

pd — Probability distribution

probability distribution object

Probability distribution, specified as a probability distribution object created using one of the following.

Function or App	Description
makedist	Create a probability distribution object using specified parameter values.
fitdist	Fit a probability distribution object to sample data.
Distribution Fitter	Fit a probability distribution to sample data using the interactive Distribution Fitter app and export the fitted object to the workspace.

Output Arguments

m — Median

scalar value

Median of the probability distribution, returned as a scalar value. The value of m is the 50th percentile of the probability distribution.

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.