Error/difference of sampling an element from a set

Question

Assume there is a set, $A_j={x_1, x_2,...,x_n}$. What should be the error associated in selecting/choosing an element from $A_j$, given each element of $A_j$ has an equal probability ($1/n$) of getting selected?

Would average provide a good estimate?

e.g., $Error=|x'-(\sum_{i=1}^{n}x_i)/n|$

The ultimate goal is to estimate the sample statistics (mean, variance) where, the sample is composed of $x'_1,x'_2,...,x'_k$ where $x'_i$ is drawn from $k$ number of sets $A_1,A_2,...,A_k$.

Answer 1

You may want to look at the link. You may report both RMSE and MAE.