Statistical analysis is the analysis of a very large number of particles / sample space where the general behaviour and trends of these particles is studied. But this also means that its probabilistic. That is, the properties of individual particles may and most definitely will deviate from the general trends. As in nuclear fission and calculation of their half lives. It doesn't seem to be possible to know whether a nucleus will split or not. And most of kinetic theory and thermodynamics seem to be statistics. The individual particles are way weirder.
So why, even though a lot of deviations from the general trend exist, statistical analysis is still used? Is it really impossible to analyze the individual particles?