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The answer explained by a youtuber I watched it a long time ago

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I believe that the distribution of your sample mean will tend towards a Gaussian distribution regardless of the underlying distribution (i.e. central limit theorem). The variance of the mean will be $\frac{\sigma^2}{N}$, where $\sigma^2$ is the variance of the underlying distribution, and $N$ is the number of data points used to calculate the mean. By the ...

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The first one is correct from the perspective of interval arithmetic. Meaning that if you are absolutely certain that each volume is within $0.05$ mL of the true value, then you are absolutely certain that the average volume is within $0.05$ mL of the true value as well. This works out for the reason you described. The second one is never correct. Dividing ...

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You may want to check your sampling with regards to the asymmetry. That suggests a bias is somehow being introduced into whatever Monte Carlo subprocesses are showing that asymmetric uncertainty, or that those subprocesses have yet to reach equilibrium. I've observed something similar when accidentally non-uniform sampling point picking on a sphere. If ...

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This is sort of more an appropriate question for Physics SE or similar, but I can help you anyway. I know of several conventions in active use. The most precise that I have seen will quote two digits of uncertainty and the two relevant uncertain digits. For example, http://physics.nist.gov/cgi-bin/cuu/Value?bg|search_for=universal_in! quotes $G$ as ...

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