We studied the stellar populations of 40 early-type galaxies using medium resolution long-slit spectroscopy along their major axes (and along the minor axis for two of them), from 10^7 Msol to 10^12 Msol (-9.2 > M_B > -22.4 mag). All the studied galaxies lie on the mass-metallicity and age-mass relations. The transition type dwarfs deviate from the latter relation having younger mean age, and the low-mass dwarf spheroidals have older ages, marking a discontinuity in the relation, possibly due to selection effects. In all mass regimes, the mean metallicity gradients are approximately -0.2 and the mean age gradients +0.1 dex per decade of radius. The individual gradients are widely spread: $ -0.1 < abla_{rm Age} < 0.4 $ and $-0.54 < abla_{[{rm Fe/H}]} < +0.2 $. We do not find evidence for a correlation between the metallicity gradient and luminosity, velocity dispersion, central age or age gradient. Likewise, we do not find a correlation between the age gradient and any other parameter in bright early-type galaxies. In faint early-types with $M_B gtrsim -17$ mag, on the other hand, we find a correlation between the age gradient and luminosity: the age gradient becomes more positive for fainter galaxies. We conclude that various physical mechanisms can lead to similar gradients and that these gradients are robust against the environmental effects. In particular, the gradients observed in dwarfs galaxies certainly survived the transformation of the progenitors through tidal harassment or/and ram-pressure stripping. The diversity of metallicity gradients amongst dwarf elliptical galaxies may reflect a plurality of progenitors morphologies. The dwarfs with steep metallicity gradients could have originated from blue compact dwarfs and those with flat profiles from dwarf irregulars and late type spirals. (Abridged)
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