  In order to fully understand the shapes of asteroids families in the
3-dimensional space of the proper elements $(a_{\rm p}, e_{\rm p}, \sin I_{\rm
p})$ it is necessary to compare observed asteroids with N-body simulations. To
this point, we describe a rigorous yet simple method which allows for a
selection of the observed asteroids, assures the same size-frequency
distribution of synthetic asteroids, accounts for a background population, and
computes a $\chi^2$ metric. We study the Eos family as an example, and we are
able to fully explain its non-isotropic features, including the distribution of
pole latitudes $\beta$. We confirm its age $t = (1.3\pm0.3)\,{\rm Gyr}$; while
this value still scales with the bulk density, it is verified by a Monte-Carlo
collisional model. The method can be applied to other populous families (Flora,
Eunomia, Hygiea , Koronis, Themis, Vesta, etc.).
