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I can not find a clear explanation for when NOT to use Bessel's correction and use N instead of N-1. As I understand it, Bessel's correction would apply to things such as clinical trials, sampling from a production line, voter polling, etc.

I am performing an experiment analyzing mass flow rate into 3 entry points. I want to analyze the deviation of the distribution into those 3 entry points and compare it to an ideal perfectly even distribution of a (relatively) known mass.

I believe I know the "true population mean" in this circumstance - its an even distribution so if I reduce everything to percentages, it would be X = 1/3 = 0.333. I believe I need to use N instead of N-1.

The complicating factors are that while I think I know the starting mass for the experiment, my scale has an instrument error associated with it. Also my measurement of mass flow rate versus time has multiple measurement instruments associated with it as well!

I guess if I boil down the question.... I need to figure out if I need to use N or N-1 for standard deviation. Does the error inherent to the measurements necessitate N-1 or does knowing my "ideal distribution" allow me to use N?

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