  We describe the use of the Frechet mean and variance in the
Billera-Holmes-Vogtmann (BHV) treespace to summarize and explore the diversity
of a set of phylogenetic trees. We show that the Frechet mean is comparable to
other summary methods, and, despite its stickiness property, is more likely to
be binary than the majority-rules consensus tree. We show that the Frechet
variance is faster and more precise than commonly used variance measures. The
Frechet mean and variance are more theoretically justified, and more robust,
than previous estimates of this type, and can be estimated reasonably
efficiently, providing a foundation for building more advanced statistical
methods and leading to applications such as mean hypothesis testing.
