Sample mean: dependence I have a question that is possibly more about language than math, but still it concerns me a lot. I understand that this question may irritate many (because it's stupid, and apparently because I am stupid too), but still I ask not to hate me too much.
We all remember the definition of sample mean:
$ {\displaystyle A={\frac {1}{n}}\sum _{i=1}^{n}a_{i}.} $
It is sum divided by size. Okay. Note that we're not talking about population mean, we're talking about sample mean.
So, today a colleague of mine uttered the following sentence:

Sample mean does not depend on sample size.

Now I'll try to explain my hesitation. As I see that there's some $ n $ that is not constant in this formula, I want to say that sample mean depends on $ n $. But as this $ n $ is fully defined by the sample itself, there is, seemingly, a sense in which sample mean does not depend on $ n $.
So the question is: is my colleague's statement true? And what's that important thing that I don't get about sample mean that makes me so confused about such a basic thing?

A clear answer would be "NO". It depends on sample size and as the number of samples goes to infinity, your sample mean will approach to the population mean.
