From left to right the second-order corrections of the uncertainties of the binary fraction (δf_bin)_corr, the velocity dispersion (δσ_c)_corr, and the mean velocity (δμ_c)_corr. The top panels show the dependency of these corrections on the velocity dispersion of the cluster (σ_c) and the lower panels show their dependency the sample size (N_obs). These corrections have been computed for the a binary fraction of 0% (blue), 50% (green), and 100% (red). They can be used to calculate the one-sigma uncertainties using Eqs. (7a)–(7c). This allows for the estimation of the accuracy with which the intrinsic velocity distribution can be measured before any radial velocity data has been taken, as long as an estimate for the velocity dispersion and binary fraction are available. The cyan lines in the left panels show the lines with δf_bin = 0.34, which is the expected uncertainty if the binary fraction is unconstrained (i.e. a flat probability distribution between 0 and 1).