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Does $5\sigma$ represent a data point that is five standard deviations from the mean? If so, suppose we come across data that is for some reason $4$ or $5$ standard deviations from the mean. Could this be determined using the $\textit{population standard deviation}$?

http://en.wikipedia.org/wiki/Standard_deviation#Basic_examples

When would it be advised to divide by $\textit{n}$ as opposed to $\textit{n-1}$, and under what conditions could someone use this method to determine the standard deviation?

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When would it be advised to divide by n as opposed to n-1 , and under what conditions could someone use this method to determine the standard deviation?

If you have the data of the (whole) population, then you divide the sum of squares by n. The definition of the term "population" is defined/explained here.

The population could be the member of a community. And the property could be the age. If you have all the data of the ages of the members, than you don´t have to estimate the standard deviation. You just calculate it. n in the denominator.

If you don´t have all the data, then you make a sample of size n. From this sample you can calculate an estimator for the standard deviation. This estimator is unbiased, if you have n-1 in the denominator, instead of n.

The sample values should be drawn independetly and with replacement.

Does 5σ represent a data point that is five standard deviations away from the mean.

If you mean $\overline x+5 \sigma$ or $\overline x-5 \sigma$, then you are correct.

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  • $\begingroup$ Calculus: Thanks for your post and your thoughtful explanation, as well as answering my multiple questions. Appreciate it! $\endgroup$ – CuriousGeorge119 Aug 3 '14 at 16:00

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