  Rate distortion theory was developed for optimizing lossy compression of
data, but it also has a lot of applications in statistics. In this paper we
will see how rate distortion theory can be used to analyze a complicated data
set involving orientations of early Islamic mosques. The analysis involves
testing, identification of outliers, choice of compression rate, calculation of
optimal reconstruction points, and assigning "descriptive confidence regions"
to the reconstruction points. In this paper the focus will be on the methods,
so the integrity of the data set and the interpretation of the results will not
be discussed.
