We use an end-to-end model of planet formation, thermodynamic evolution, and atmospheric escape to investigate how the statistical imprints of evaporation depend on the bulk composition of planetary cores (rocky versus icy). We find that the population-wide imprints like the location of the "evaporation valley" in the distance-radius plane and the corresponding bimodal radius distribution clearly differ depending on the bulk composition of the cores. Comparison with the observed position of the valley suggests that close-in low-mass Kepler planets have a predominantly Earth-like rocky composition. Combined with the excess of period ratios outside of MMR, this suggests that low-mass Kepler planets formed inside of the water iceline but were still undergoing orbital migration. The core radius becomes visible for planets losing all primordial H/He. For planets in this " triangle of evaporation" in the distance-radius plane, the degeneracy in composition is reduced. In the observed planetary mass-mean density diagram, we identify a trend to more volatile-rich compositions with an increasing radius (R/R-circle plus less than or similar to 1.6 rocky; 1.6-3.0 ices, and/or H/He; greater than or similar to 3: H/He). The mass-density diagram contains important information about formation and evolution. Its characteristic broken V-shape reveals the transitions from solid planets to low-mass core-dominated planets with H/He and finally to gas-dominated giants. Evaporation causes the density and orbital distance to be anticorrelated for low-mass planets in contrast to giants, where closer-in planets are less dense, likely due to inflation. The temporal evolution of the statistical properties reported here will be of interest for the PLATO 2.0 mission, which will observe the temporal dimension.