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Ok, we all know that if a quantity T is measured N times, then all measurements have the same standard deviation (SD). Now, with this assumption one can derive the width of the average to get SD/sqrt(N).

I have often encountered a dataset D, where each measurement has been assigned no SD. Then one finds the SD for the whole dataset, and then the author uses SD/sqrt(N) to find the width of the average of D.

My question is: In these cases, then what justifies that SD found from the whole dataset D can be assumed to be valid for each single measurements, such that one can use SD/sqrt(N)?

I hope you understand.

Best,

Niles.

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# Uncertainties of averages

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