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?

Mean versus average


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


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().

