pd — Probability distribution probability distribution object

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.

Interquartile range of the probability distribution, returned
as a scalar value. The value of r is the difference
between the values of the 75th and 25th percentile of the probability
distribution.

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

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

Crete 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 =
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.