Velocity dispersion measurements for simulated spectra. Left panel: Relative offset of the recovered velocity dispersion with respect to the true value as a function of the S/N. We show the median relative uncertainty from Eq. (A.1) as a black line. Right panel: Absolute offset between the recovered and the true velocity dispersion values as a function of the input velocity dispersion. The points are colour-coded by the corresponding spectral S/N.