Is there a theorem (etc.) that states the average skewness of repeated samples will approach the skewness of the population? If so, I need the name.
I confirmed my suspicion that this is true. I created a dataset (n=30,000) by joining normal distributions, such that is looks "normal-like," with a skew of about -1. 100 repeated samplings of 500 has an average skewness of -1. Also, the means of the samples are a normal distribution - of course (central limit theorem).