  The arithmetic mean plays a central role in science and technology, being
directly related to the concepts of statistical expectance and centrality. Yet,
it is highly susceptible to the presence of ouliers or biased interference in
the original dataset to which it is applied. Described recently, the concept of
similarity means has been preliminary found to have marked robustness to those
same effects, especially when adopting the Jaccard similarity index. The
present work is aimed at investigating further the properties of similarity
means, especially regarding their range, translating and scaling properties,
sensitivity and robustness to outliers. Several interesting contributions are
reported, including an effective algorithm for obtaining the similarity mean,
the analytic and experimental identification of a number of properties, as well
as the confirmation of the potential stability of the similarity mean to the
presence of outliers. The present work also describes an application
case-example in which the Jaccard similarity is succesfully employed to study
cycles of sunspots, with interesting results.
