Statistics imply a model. Mean and standard deviation, for instance, have meaning only in the context of the model you are fitting the data. As with any tool, it can be used to negate or perpetuate prejudices depending on who is putting together the statistical model and for what purpose. What statistics does, in basic, is take a whole mess of data and condense that data into the parameters of an a priori chosen model. Statistics is a method of analyzing data and has never been without controversy. Algebra, calculus, etc. are on a higher plane of basic mathematical building blocks building out from axioms through proofs.

Consider the Two Envelopes Problem. You have two envelops on the table in front of you. One contains double the money of the other. You choose one. Opening it, you find $20. You have the option of keeping that or choosing the other, which may have $10 (half your envelop), or $40 (double your envelop). An expected value proposition tells you to switch, even though intuition says it's 50/50 whether you gain from a switch. Why? Because the average value of switching is: 1/2*($40+$10)=$25, which is greater than your $20 in hand. Where did this calculation go wrong?

Using "average" to be "mean" as above, implies the data fits a normal distribution model. The problem describes a situation that is far from a normal distribution. Hence the data "mean" tells you nothing in this case; doesn't even have a meaning. This is what I mean when I say statistics implies an a priori model. Every time you make a statistical manipulation to the data, you are throwing information away. Just keep this in mind when you use these models. There are lots of assumptions built into statistical methods.