iqr

Create a standard normal distribution object with the mean, $$\mu$$, equal to 0 and the standard deviation, $$\sigma$$, equal to 1.

pd = makedist('Normal','mu',0,'sigma',1);

Compute the interquartile range of the standard normal distribution.

r = iqr(pd)

r = 
1.3490

The returned value is the difference between the 75th and the 25th percentile values for the distribution. This is equivalent to computing the difference between the inverse cumulative distribution function (icdf) values at the probabilities y equal to 0.75 and 0.25.

r2 = icdf(pd,0.75) - icdf(pd,0.25)

r2 = 
1.3490

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 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 = 1×2

   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.