Number distributions of the LRG and CMASS galaxies over redshift. The width of redshift in the histograms is Δz = 3.25 × 10⁻³. Also shown are the redshift ranges enclosed by spheres with a series of radii from 50 to 300 h⁻¹ Mpc, centered at z_cen = 0.35 for LRG and z_cen = 0.52 for CMASS (denoted as vertical dotted lines). For radii of 250 and 300 h⁻¹ Mpc in the case of the CMASS sample, the redshift ranges have been shifted to the higher redshift to include more galaxies within the range specified.