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Correct standard deviation formula

Expert replies
Source: — Problem Solving |

by Testluv » Sat Apr 16, 2011 10:17 pm
The answer is: you don't need to know any formula for standard deviation of the GMAT: just a thorough understanding of the concept. I have yet to encounter an official question that required knowledge of the formula.

(In any case, the formulae that are relevant would be "a" and "b". "b" if "n" represents the entire data and "a" if it is just a part (a "sample") of the data).
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by vishalchaudhury » Sat Apr 16, 2011 11:33 pm
Thanks,

I could not understand ""b" if "n" represents the entire data and "a" if it is just a part (a "sample") of the data)."
If we are asked to find SD for say the data set 2345,7,9,23,67,8,23,54 then we use formula b
and if we are asked to find SD for a subset say 2345,7,9,23 then we use formula a?

But why can't we simply use formula b for the subset as well.
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by Ian Stewart » Sun Apr 17, 2011 10:35 am
Those formulas are just going to be confusing; the notation is completely different from anything you'll ever see on the GMAT. Technically, it's version (b) that you would use on the GMAT; you can ignore the others. But, as Testluv says, you never need to compute standard deviation on the GMAT. You *do* need to understand what standard deviation *measures*, so you need to be able to judge whether the set {0, 5, 5, 10} has a larger standard deviation than the set {99, 100, 100, 101} (it does, because elements in the first set tend to be further from the mean).

When you calculate standard deviation, the steps are as follows (and be aware that if you find yourself computing a standard deviation on the GMAT, you've missed something - it is *never* required, so what follows is for interest only). Let's take one of those rare sets that will actually give us an integer answer for standard deviation - {2, 3, 4, 5, 6, 7, 8}.

* You first find the mean, which is 5.
* You then find how far each element is from the mean and list those distances: 3, 2, 1, 0, 1, 2, 3.
* Now we square each of these numbers and average the result: (3^2 + 2^2 + 1^2 + 0^2 + 1^2 + 2^2 + 3^2)/7 = 28/7 = 4.
* Finally we take the square root of this average: sqrt(4) = 2 = standard deviation

Notice in the third step, we divide by 7, the number of elements in the set. In your formula sheet, this is n; we do not subtract 1 from n.
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