Median Statistics Estimate of the Distance to M87

Abstract

de Grijs and Bono compiled 211 independent measurements of the distance to galaxy M87 in the Virgo cluster from 15 different tracers and reported the arithmetic mean of a subset of this compilation as the best estimate of the distance. We compute three different central estimates -- the arithmetic mean, weighted mean, and the median -- and corresponding statistical uncertainty for the full data set as well as two sub-compilations. We find that for all three central estimates the error distributions show that the data sets are significantly non-Gaussian. As a result, we conclude that that the median is the most reliable of the three central estimates, as median statistics does not assume Gaussianity. We use median statistics to determine the systematic error on the distance by analyzing the scatter in the 15 tracer subgroup distances. From the 211 distance measurements, we recommend a summary M87 distance modulus of $31.08^{+0.04}_{-0.05}$ (statistical) ${}^{+0.04}_{-0.06}$ (systematic) mag, or combining the two errors in quadrature $31.08^{+0.06}_{-0.08}$ mag, rounded to $16.4^{+0.5}_{-0.6}$ Mpc, all at $68.27\%$ significance.