We investigate the Mg-sigma and <Fe>-sigma relations in a sample of 72 early-type galaxies drawn mostly from cluster and group environments using a homogeneous data-set which is well-calibrated onto the Lick/IDS system. The small intrinsic scatter in Mg at a given sigma gives upper limits on the spread in age and metallicity of 49% and 32% respectively, if the spread is attributed to one quantity only and if the variations in age and metallicity are uncorrelated. The age/metallicity distribution as inferred from the Hbeta vs <Fe> diagnostic diagram reinforces this conclusion, as we find mostly galaxies with large luminosity weighted ages spanning a range in metallicity. In our sample we do not find significant evidence for an anti-correlation of ages and metallicities which would keep the index-sigma relations tight while hiding a large spread in age and metallicity. As a result of correlated errors in the age-metallicity plane, a mild age-metallicity anti-correlation cannot be completely ruled out given the current data. Correcting the line-strengths indices for non-solar abundance ratios following the recent paper by Trager et al., leads to higher mean metallicity and slightly younger age estimates while preserving the metallicity sequence. The [Mg/Fe] ratio is mildly correlated with the central velocity dispersion and ranges from [Mg/Fe]=0.05 to 0.3 for galaxies with sigma > 100 km/s. Under the assumption that there is no age gradient along the index-sigma relations, the abundance-ratio corrected Mg-sigma, <Fe>-sigma and Hbeta-sigma relations give consistent estimates of Delta [M/H]/ Delta log sigma = 0.9 (+- 0.1). The slope of the Hbeta-sigma relation limits a potential age trend as a function of sigma to 2-3 Gyrs along the sequence.(abriged)
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