In our Solar system, the density of major planets varies from 0.7 g/cm3 (Saturn) to 5.5 g/cm3 (Earth).
For exoplanets, the density varies from very low (0.03 g/cm3 for Kepler-51x) to very high (77.7 g/cm3 for Kepler-131c, data according to NASA Exoplanet Archive).
We know that bodies with low density are composed of gas and others are rocky planets. Wikipedia provides some approximations about it.
Is there any detailed classification of planetary bodies by density? A classification that would say, for example, that the density below 1.5 g/cm3 corresponds to a gas planet; between 1.5 and 3 are icy; between 3 and 8 are rocky; above 8 g/cm3 are even more rocky etc...
Would such a classification make sense?
If it exists, which are the numeric bounds for the different types of bodies?