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This page from mathsisfun.com provides several examples showing how to calculate the mean of a set of numbers. One of the examples involves negative numbers. At the end, you can link to "the mean machine" or take a quiz. For a more advanced discussion about mean, see http://www.onlinemathlearning.com/mean.html.
When most people say "average" they are talking about the "mean" of a data set, but in statistics, "average" can refer to the mean, the median and the mode.
Some data sets have no mode, and some have more than one mode!
Read about the median at mathsisfun.com. At the bottom of this page, you can try finding the median of different data sets, and you can take a quiz on medians. For a more advanced discussion of median, see www.onlinemathlearning.com/median.html.