I've commented from the time to time that the standard deviation is the problem child of statistics because, relative to what introductory statistic students have done before, it is calculationally intense.
Its calculation can be simplified if we make a study of the quantity that I called "Fred" in one of the earlier entries. It is also sometimes called the second moment of x and referred to by S subscript xx. When I say this aloud, it sounds like "sex, sex, sex." That might make it more amusing to you, but it might create strange associations with math for you. It might be best not to think on this too much.
Below I've worked out the calculations that simplify Sxx. If you are geeky enough to want to see how it's done, you are probably geeky enough to follow them. If not, let me know.