# Is it possible to estimate population mean from sample mean without knowing standard deviation or variance?

I started doing exercises from chapter about Point estimation and right at the beginning I hit a hurdle.

I was provided three bits of information, sample mean, size of the sample and size of the population. The wording of the exercise is ambiguous. It can either mean that I should guess the population mean or that I should estimate it, that is, reach the value using formulas.

The problem is I can't find single formula for estimating the population mean that does not rely on standard deviation or variables that are computed from standard deviation. Also my intuition tells me that there is no way to do that since I could obtain same sample mean from infinite number of other possible populations and without knowing the deviation I have no way to trim down this set.

The question is: Am I right? Is it impossible to estimate population mean without deviation? Or am I missing some part of the picture?

## 2 Answers

The obvious estimator of the population mean is the sample mean itself. Why do you think you need the standard deviation for that?

Maybe I'm missing something really obvious but a quite reasonable estimate of the population mean is the sample mean. Without access to other data (variance, sampling methods, etc) you cannot say anything about how good an estimate the sample mean is but it is still the best estimate you have.