# Documentation

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# median

Class: prob.TruncatableDistribution
Package: prob

Median of probability distribution object

## Syntax

```m = median(pd) ```

## Description

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

## Input Arguments

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Probability distribution, specified as a probability distribution object. Create a probability distribution object with specified parameter values using `makedist`. Alternatively, for fittable distributions, create a probability distribution object by fitting it to data using `fitdist` or the Distribution Fitting app.

## Output Arguments

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

## Examples

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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 will be equal to the mean, `mu`.

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; pdfx = pdf(pd,x); plot(x,pdfx) ```