We present measurements of Fe, Mg, Si, Ca, and Ti abundances for 388 radial velocity member stars in the Sculptor dwarf spheroidal galaxy (dSph), a satellite of the Milky Way (MW). This is the largest sample of individual α element (Mg, Si, Ca, and Ti) abundance measurements in any single dSph. The measurements are made from Keck/Deep Imaging Multi-Object Spectrometer medium-resolution spectra (6400–9000 Å, R∼ 6500). Based on comparisons to published high-resolution (R≳ 20,000) spectroscopic measurements, our measurements have uncertainties of σ [Fe/H]= 0.14 and σ [α/Fe]= 0.13. The Sculptor [Fe/H] distribution has a mean<[Fe/H]>=− 1.58 and is asymmetric with a long, metal-poor tail, indicative of a history of extended star formation. Sculptor has a larger fraction of stars with [Fe/H]<− 2 than the MW halo. We have discovered one star with [Fe/H]=− 3.80±0.28, which is the most metal-poor star known anywhere except the MW halo, but high-resolution spectroscopy is needed to measure this star's detailed abundances. As has been previously reported based on high-resolution spectroscopy,[α/Fe] in Sculptor falls as [Fe/H] increases. The metal-rich stars ([Fe/H]∼− 1.5) have lower [α/Fe] than Galactic halo field stars of comparable metallicity. This indicates that star formation proceeded more gradually in Sculptor than in the Galactic halo. We also observe radial abundance gradients of− 0.030±0.003 dex arcmin− 1 in [Fe/H] and+ 0.013±0.003 dex arcmin− 1 in [α/Fe] out to 11 arcmin (275 pc). Together, these measurements cast Sculptor and possibly other surviving dSphs as representative of the dwarf galaxies from which the metal-poor tail of the Galactic halo formed.