Re: What exactly is standard deviation?
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For instance, since 68% of people's IQ score falls between 85-115, then 15 is determined as the standard deviation, right?
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Your statement is true only for Gaussian, aka normal, distributed random variables. In general, standard deviation is the square root of the variance, i.e. E[(X- E[X])^2]^.5. Variance can be thought of as a measure of the randomness of a random quantity. The reason that your view of SD is quite common is that many things are assumed to be Gaussian, especially if they are the result of some combination of a large number of random variables (like IQ.) This assumption is based on the Central Limit Theorem, which is often miss applied.
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