BACKGROUND & QUESTION:
Year after year, the annual statistical convention is held in the same city. This metropolis has 26 pubs, each named by an alphabet letter: A, B, C, … , Y, Z. The statisticians who are nice, kind, & considerate people go to a wide variety of these “drinking holes.” The mean statisticians, however, patronize just one of them. Which one?
ANSWER: The X-Bar
(This little effort at statistical humor comes from S. Huck)
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Beyond the Joke:
In statistics, the concept or numerical value of the arithmetic mean can be symbolized in various ways.
Many people use the letter M (often capitalized and italicized) to represent the arithmetic mean. A second way to do this is with the lower-case Greek letter, mu. (In several textbooks, M is used to represent the sample mean whereas mu designates the population mean.)
A third way to symbolize the arithmetic mean is with the letter X accompanied by a short, horizontal line positioned directly above the X. This line is referred to as a “bar,” and the entire symbol is read as “X-bar.”
In written statistical discussions, a bar can be positioned above letters (or symbols) other than the letter X. When this occurs, the bar indicates that the arithmetic mean has been (or should be) computed for the various numerical values of the variable represented by whatever letter or symbol has the bar above it. For example, if you see the lower-case letter r with a bar above it, you should refer to it as “r-bar” and guess that it represents the mean of a group of correlation coefficients.