Most frequent value analysis of distance measurements to M87.

We reanalyse the recent compilation of distance measurements to M87 by collecting the data from published literature. Different from the traditional statistical methods, based on the principle of minimum information loss, we use a robust most frequent value (MFV) procedure to estimate the distance to M87, irrespective of the Gaussian or non-Gaussian distributions. The MFV-based robust estimate for the M87 distance modulus is given by |$31.09^{+0.04}_{-0.03}$| (statistical) |$^{+0.05}_{-0.07}$| (systematic) mag corresponding to a 68.27 per cent confidence interval, whereas the result of combining the two uncertainties in quadrature is |$31.09^{+0.06}_{-0.08}$|  mag. We also construct the error distributions of M87 distance moduli values according to the weighted mean, median, and MFV, which is non-Gaussian. This demonstrates that the MFV method offers a more accurate and robust estimate of the distance to M87 compared to methods that depend on the unfulfilled assumption of Gaussianity. [ABSTRACT FROM AUTHOR]