Yes, but such things as weather forecast for a week are not that much statistical. And yet we fail even to accurately predict whether it is going to rain tomorrow. I understand that one can make global prediction without having to predict every minor statistical detail, but if one cannot predict minor details, then wouldn't the global predictions have to be taken with a grain of salt? We don't need to know all the electron spins within each atom to be able to predict a temperature in the room 5 minutes after turning the heater on, but we can measure those spins within a few atoms, if we really want it; or, at the very least, we know how it can be done in principle, by using our existing theory.
Yet, it seems to me, we know much more about electrons within atoms, than we do about local weather. Which is strange to me personally, given that weather is happening on macroscopic scale and, in theory, shouldn't require the precision anywhere near what we need for atomic level measurements, making it easier to do in principle.