# How to determine population range based on a sample

How to determine the range of values of the population (with some confidence, e.g. 95%) based on a sample?

I thought about one approach to follow the 68-95-99 rule, based on population mean estimate and population standard deviation estimate calculated from a sample. But those are only estimates, we don't know the real population mean, we have only 95% confidence interval for it. Thus, I am not sure how to correctly apply this rule. Let's assume normal distribution for simplicity (but it would also be interesting to know if there is a simple answer without assuming normality.)

EDIT: based on one of the answers below, I need to clarify that I am not interested in knowing the range that contains 100% of population values (which is infinity, and is not useful), but the one that contains 95% (or 99% etc.) of population values.

• In order to estimate the range of the population you will need its mean and standard deviation and, since you don't know the true values, you will need to use the estimated values. There's nothing wrong with using other estimates when estimating something else, so long as you make the appropriate adjustments when finding variance etc. I should note though that there may be a formal method for this which I'm not aware of, hence I'm only commenting. Commented Sep 5, 2016 at 1:45
• en.wikipedia.org/wiki/German_tank_problem Commented Sep 5, 2016 at 5:21
• This question is possibly related. Commented Sep 6, 2016 at 13:57