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The thing about the average i'm that curious about is for example: the average height of 5 people turns out to be say 6 feet. suppose here it turns out that NONE of the people have a height of exactly 6 feet.

So the "average" (expectation value) doesn't correspond to an actual physical value that any one person has.

So why is it that when we find the expectation value (of say position) on a particle it corresponds to a physical value that we can measure; when this value doesn't (necessarily) correspond to any one actual value that the particle has?

I think the root of my problem is; how is it that the square of our wave function corresponds to the probability of finding that particle (at a given time and place) ?

Perhaps i'm confusing a single measurement on a particle compared to multiple measurements on a particle in multiple equally prepared states??

Anyways any clarification would be appreciated, Thanks