median

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.

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)