What is the difference between "mean value" and "average"? Wikipedia explains:

For a data set, the mean is the sum of the values divided by the number of values.

This definition however corresponds to what I call "average" (at least that's what I remember learning). Yet Wikipedia once more quotes:

There are other statistical measures that use samples that some people confuse with averages - including 'median' and 'mode'. 

Now that's confusing. Are "mean value" and "average" different from one another? If so how?
 A: Mean and average are generally used interchangeably (although I've seen them used as referring to population versus empirical).
They, like median and mode, are measures of central tendency, but in many cases, the other two are different.
A: The mean you described (the arithmetic mean) is what people typically intend when they say "mean" and, yes, that is the same as average. The only ambiguity that can occur is when someone is using a different type of mean, such as the geometric mean or the harmonic mean, but I think it is implicit from your question that you were talking about the arithmetic mean
A: Mean versus average


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*The mean most commonly refers to the arithmetic mean, but may refer to some other form of mean, such as harmonic or geometric (see the Wikipedia article). Thus, when used without qualification, I think most people would assume that "mean" refers to the arithmetic mean.

*Average has many meanings, some of which are much less mathematical than the term "mean". Even within the context of numerical summaries, "average" can refer to a broad range of measures of central tendency.

*Thus, the arithmetic mean is one type of average.
Arguably, when used without qualification the average of a numeric variable often is meant to refer to the arithmetic mean.


Side point


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*It is interesting to observe that Excel uses the sloppier but more accessible name of AVERAGE() for its arithmetic mean function, where R uses mean().

A: I see "average" and "mean" used mostly as synonyms. One author who draws a clear distinction is Donald Wheeler, in "Advanced Topics in Statistical Quality Control." He declares that the "average" is a statistic determined by some arithmetic procedure, whereas "mean" is a parameter, specifying location of a distribution. By way of example, he writes that one could calculate an "average" telephone number, which would be meaningless (pun?). The average (a statistic) is an unbiased estimate of the mean (a parameter).
A: There are several "averages."  Just think of this trick question: "What is the probability that the next person you meet has more than the average number of arms?"
The "mean" or "arithmetic mean" or "arithmetic average" is one average that you learned in the past.  But the median (the value with half the observations greater and half less than it), the mode (the most common value), the geometric mean (multiply the values then take the nth root), the harmonic mean (the reciprocal of the mean of the reciprocals of the data), and others all fall under the general term "average."
