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By itself, very little, apart from the fact that it is somewhere in the middle of the spread of data. For example, the mean of the data set comprising {1, 1, 1, 1, 1, 1, 1, 1, 2, 9990} is 1000. Also, the mean of the set {1000, 1000} is also 1000. The sets are hardly similar, though.
Variance is the squared deviation from the mean. (X bar - X data)^2
That depends on the context (or how it is used in a sentence). Based on the fact could mean that if that "fact" is true then everything else mentioned is true. If the fact is false, then everything else may not be true. For example, if I said "these figures are based on the fact that the same discounts are available for the rest of the year". This would mean, if the same discounts were offered, those figures would be correct. If not, those figures would not mean anything. If it was used as "based on fact", this could have a different meaning. This statement is mainly used when referring to films or books. Used in a sentence, this would mean that the story is similar to that of a true story, but some fictional parts may have been added or characters may have changed.
mean does not mean the center of the data
what do you mean by data assembly?