As I was reading through my notes, I came across this formula. It states that for independent and iid random variables $X_{1},X_{2}...X_{n}...$ with the same mean $\mu$ and variance $\sigma$,
$$\bar{X}_{n} = \sum_{i = 1}^{n}X_i$$
However, this is not in line with what I read for other formulae for the mean, which normally has a $\frac{1}{n}$ before the entire summation.
It also doesn't seem to make any logical sense to me. If I add up all the random variables which have mean $\mu$, wouldn't that just make it $n\mu$? So shouldn't I have a $\frac{1}{n}$ at the front to make it $\mu$?