Hipparcos astrometric data and Tycho photometry together with radial velocities (mainly from Coravel) are used to calibrate luminosity, kinematical parameters and scale height of Barium stars and to classify them. We improve the results of a previous paper (where we used data from the Hipparcos Input Catalogue), and show that Ba stars are an inhomogeneous group. Five distinct classes have been found, namely, some halo stars and four groups belonging to disk population: roughly supergiants, two groups of giants (one on the giant branch, the other at the clump location) and dwarfs, with a few subgiants mixed with them. The confirmed or suspected duplicity, the variability and the range of known orbital periods found in each group give coherent results supporting the scenario for Ba stars as moderately massive binary stars in any evolutionary stage but all previously enriched in Barium from a more evolved companion. The presence in the sample of a certain number of 'false' Barium stars (supergiants with Ba line enhanced by a gravity/luminosity effect or AGE stars with intrinsically strong barium lines) is confirmed.