  We use rigorous numerical techniques to compute a lower bound for the
exponent of expansivity outside a neighborhood of the critical point for
thousands of intervals of parameter values in the quadratic family. We compute
a possibly small radius of the critical neighborhood, and a lower bound for the
corresponding expansivity exponent outside this neighborhood, valid for all the
parameters in each of the intervals. We illustrate and study the distribution
of the radii and these exponents. The results of our computations are
mathematically rigorous. The source code of the software and the results of the
computations are made publicly available at
http://www.pawelpilarczyk.com/quadratic/..
