Top figure: velocity dispersion (top panel) and velocity dispersion uncertainty (bottom panel) as a function of distance D from the Sun. Blue, red and green curves correspond to the velocity dispersions in the aziumthal, radial and vertical directions, as indicated in the legend. Bottom panel: solid lines indicate the mean relation, and the colour-shaded areas indicate the 1σ uncertainty, estimated through 100 random realisations, from the uncertainties on the observables (see text). These uncertainties are then reported in the bottom panel. Middle and bottom figures: as above, but now velocity dispersions and corresponding uncertainties are shown as a function of [Fe/H] and [Mg/Fe], respectively. In all plots, velocities are in units of km s⁻¹.