  Topological Data Analysis (TDA) provides a toolkit for the study of the shape
of high dimensional and complex data. While operating on a space of persistence
diagrams is cumbersome, persistence norms provide a simple real value measure
of multivariate data which is seeing greater adoption within finance. A growing
literature seeks links between persistence norms and the summary statistics of
the data being analysed. This short note targets the demonstration of
differences in the persistence norms of the Datasaurus datasets of Matejka and
Fitzmaurice. We show that persistence norms can be used as additional measures
that often discriminate datasets with the same collection of summary
statistics. Treating each of the data sets as a point cloud we construct the
$L_1$ and $L_2$ persistence norms in dimensions 0 and 1. We show multivariate
distributions with identical covariance and correlation matrices can have
considerably different persistence norms. Through the example, we remind users
of persistence norms of the importance of checking the distribution of the
point clouds from which the norms are constructed.
