Why is the standard deviation of mean a good estimate for theuncertainty of a si

Question

Why is the standard deviation of mean a good estimate for theuncertainty of a single measurement with respect to the truemean? This is related to a lab, and I am having a brain fart.Any help would be great! Is it because the SDOM has the denominator N for Nsamples? Why is the standard deviation of mean a good estimate for theuncertainty of a single measurement with respect to the truemean? This is related to a lab, and I am having a brain fart.Any help would be great! Is it because the SDOM has the denominator N for Nsamples?

Explanation / Answer

Often, the uncertainty of a measurement is found by repeating themeasurement enough times to get a good estimate of the standarddeviation of the values. Then, any single value has an uncertaintyequal to the standard deviation. However, if the values areaveraged, then the mean measurement value has a much smalleruncertainty, equal to the standard error of the mean, which is thestandard deviation divided by the square root of the number ofmeasurements.

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