Radio power–mass diagram and volume distribution of the radio halos of the statistical sample. Left: P_1.4 GHz − M₅₀₀ diagram. Black filled circles represent radio halos; green empty circles represent USSRHs and candidate USSRHs. The small radio halos are labelled. The best-fit relation obtained with the BCES Y|X method and excluding USSRHs is shown with its 95% confidence region. The best-fit parameters are B = 3.92 ± 0.79 and A = −0.15 ± 0.10. Right: distribution of the volumes of the radio halos, scaled for R₅₀₀. The four clusters lying on the left tail, separated from the main distribution, are A3411, Z0634, A2218, and A1689.