Distributions of red shift z, r-band absolute magnitude M_r and stellar mass M_* of LRGs in our study. The full sample consists of 37 621 LRGs from a combination of an SDSS LOWZ sample that dominates the LRG population at z ≲ 0.4 and the CMASS sample that dominates at z = 0.4–0.7 (left-hand panel). Considering only LRGs with sufficiently high S/N background QSO spectra for detecting Mg ii absorbers as weak as W₀ = 0.3 Å, yields a total sample of 13 330 LRGs, 1575 of which are [O ii]-emitting (open dashed histograms) and 11 755 are passive LRGs with no trace of [O ii] emission at more than a 2σ level of significance (open red histograms). The red-shift distributions of these LRGs show that the W₀ = 0.3 Å cut removes a significant fraction of LRGs from the LOWZ sample, due to the rapidly declining throughput at λ ≲ 4000 Å of the SDSS spectrograph (Smee et al. 2013) that prohibited us from detecting relatively weak Mg ii absorption features at z ≲ 0.4. All three LRG samples share similar distributions in M_r (middle panel) and M_* (right-hand panel).