Upper panel: the scaling relation between the natural logarithm of the observed velocity dispersion of groups ln (σ_v,obs km⁻¹ s) determined using their spec-z members within r_200c and the natural logarithm of the X-ray luminosity of groups ln (L_x erg⁻¹ s) at z <  1.0 in COSMOS (blue points with associated errors). We also added axes showing the 10-base logarithmic scale. The highlighted orange area shows ±1σ uncertainties around the mean scaling relation (white dashed line). The black lines are a set of 50 different realisations, drawn from the multivariate Gaussian distribution of the parameters () and the scatter covariance matrix is estimated from the MCMC chain. Lower panel: the one- and two dimensional marginalised posterior distributions of parameters of the scaling relation (Eq. (4)), shown as 68% and 95% credible regions.