Distributions of the dispersion of polarization position angles (blue) and the polarization fraction (red) as a function of the normalized column density , for all the cores. The solid lines and points represent the running mean of and ; the associated shaded areas are ± the standard deviation of each bin. The dashed lines are the linear fits, which are linear regressions done in the logarithmic space, whose slopes and uncertainties are calculated the same way as in Fig. 4.