Integrated number of radio halos within a given redshift expected in the NVSS follow-up of the XBACS clusters (dashed line) compared with the observed values (black points) within z = 0.1 and z = 0.2 taken from Giovannini et al. (1999). The expected numbers of halos are computed by consider f_min(z) given by Eq. (9) with ξ₁ = 3 (short dashed line), and by Eq. (11) with ξ₂ = 10 (long dashed line).