Solved – Finding the mean and standard deviation of an unknown distribution from a sample

I am interested in finding the mean and standard deviation of the whole distribution by looking only at a random sample. I don't know anything else about the distribution (for example I don't know if the distribution is normal or not). Is what I'm asking even possible?

Sure, your best guess of the population mean is your sample mean, and the same is true for the standard deviation (assuming you use $sqrt{frac{sum (x_i-bar{x})^2}{n-1}}$) and not divide by just $n$).

There are distributions where the mean or standard deviation are less meaningful or even undefined, but that is up to you to decide. Also inferences may be more difficult with some distributions.

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