Histogram of the error distributions using Cepheid tracers in ﹩| {N}_{\sigma }| =0.1﹩ bins (with the exception of the last bin with ﹩5\leqslant | {N}_{\sigma }| \leqslant 6﹩). The solid black line represents the expected Gaussian probabilities for 81 measurements and the dotted blue (dashed red) line is the number of ﹩| {N}_{\sigma }| ﹩ values in each bin for the weighted mean (median) case.