Hi 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.