The Meaning Of The Mean

Bob Carpenter has a few enlightening thoughts on the distinctions between 1) the sample mean, 2) the expected value of a random variable, and 3) the mean of a distribution. I've long been confused by the difference between the mean and expected value, and his trichotomy helps alleviate my confusion. With that in mind, I changed the intro of the article mean, which had remained static since the dawn of time (2001, when the page was created).

Of the major subjects on Wikipedia, statistics seems to be the most convoluted. My two explanations for this are that 1) there are so many schools that disagree on fundamental interpretations (likelihood, non-parametric, empirical Bayesian, objective Bayesian, etc), and 2) many practitioners are so busy with applications that they don't have time to reconcile their disagreements.