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It is my understanding that the Uncertainty Principle deals with a single event (particle). It is also my understanding that quantum physics contains a lot of statistics (probability).

The question is: in the area of probability, a population is required and the equation contains a denominator of n-1. From this I assume that statistics of this kind cannot apply to a “singularity”; that is, a singular thing. For example statistics does not apply to a singular individual.

If the Heisenberg Uncertainty Principle applies to a singular “particle”, what kind of statistics is used, if any?

Thank you in advance.