Why is the expected value of any data point in the sample equal to population mean? Suppose we have a distribution of heights of all males in a country.
Let population size = N.
Now, I take a sample of 100 males = {h1,h2,h3,....h100}
How is the expected value of any data point, i.e., E(h1) = E(h2) = ..E(h100) = population mean?
NOTE:  Every individual in the population equally likely to be included in the sample.

Let $X_1,\cdots ,X_{100}\overset{iid}{\sim} F_X(x)$ for some distribution $F_X(x)$ that has an expected value $\mu$.
Since $X_1$ is distributed as $F_X(x)$, $\mathbb E[X_1]=\mu$. Since $X_2$ is distributed as $F_X(x)$,…
In the absence of other information about the subject, the value that you expect is the population value.
