We have three ambiguous tags average, expectation and means. They are often used for probability and statistics problems. The tag expected-value has been synonymized with probability. The current tag excerpts and info for these three tags are not clear enough.
- The average tag includes arithmetic means and its tag info involves means.
In its most general definition, an average is a summary of a set of values. Normally it refers to the arithmetic mean, but other means may be employed (geometric, harmonic, etc.) or a transformation may be applied before and after taking a mean (e.g. root-mean-square).
- The means tag info involves arithmetic means and expected-value.
In probability and statistics, mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution. For a data set, refers to a central value of a discrete set of numbers: specifically, the sum of the values divided by the number of values. Reference: Wikipedia.
For a finite population, the population mean of a property is equal to the arithmetic mean of the given property while considering every member of the population.
- The expectation tag info is missing. The "computations" in its tag excerpt give rise to the expected-value of probability-distributions?
For questions about the expectation of a random variable: computations, upper/lower bounds, etc.
- Synonymize means, expectation and expected-value as the first sentence in the means tag info suggest.
- Use the average tag for non-statistics questions which don't involve probability-distributions.
Edit in response to comments:
- I had proposed to synonymize probability and expectation before I posted this question since the former is a synonym of expected-value. However, from the comments under this question, it seems that that doesn't help sorting questions. Unluckily, there's no way to retract this suggestion.
Therefore, please downvote this so that it will disappear.It has been deleted thanks to the two users who downvoted this.
- Another proposal is to synonymize elementary-probability with probability. That's off-topic in this question.