Assume there are three groups of 2-dimensional coordinates

data = RandomVariate[NormalDistribution[#, .25], {15, 2}] & /@ Range[3];

Is there a way to ListPlot these data points just like

ListPlot[data, PlotStyle -> {Red, Blue, Green}]

![][1]

but instead of the dots with the result of an integer-valued function, e.g. Round[Norm[#]]&, shown in the according colour?

I already had a look at this and that question, but wasn't able to modify the answers to obtain the desired result. [1]: https://i.sstatic.net/CV9BD.png