The effect of the number of systems on the HBM results for a synthetic sample whose properties were generated with realistic uncertainties. Here, we enforced |${0< i_{\mathrm{d}}< 90^{\circ }}$| following Section 2.6.1. The panels show |$\mu$| (top) and |$\sigma$| (bottom) versus N for 5–150 systems. The dotted lines mark the input |$\mu$| and |$\sigma$| used to generate the parent alignment distribution of |$0^{\circ }$| and |$20^{\circ }$|⁠, respectively. The underestimation is most clearly seen in |$\sigma$| at large N where uncertainties are smaller. Both |$\mu$| and |$\sigma$| vary around their expected values by more than their uncertainties, especially at larger N. This is likely because we assume all the individual |$\alpha _n^{\prime }$| estimates are Gaussian.