Standard deviation σ of the Gaussian noise distribution (vertical axis) vs. noise-free average unsigned vertical flux density, determined from least-squares fits to the randomly selected 320 MDI magnetograms, assuming a cancellation exponent κ = 0.13. The filled circles have been obtained from magnetograms recorded with 5-min integration, the open circles from magnetograms with 1-min integration. The solid horizontal lines at 18.8 and 33.2 G represent the average values of σ for the two populations. For comparison the corresponding upper limits to the noise levels as derived from the analysis of Liu et al. (2012) are given as the dotted lines.