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