What exactly is standard deviation?

[Cased Heel]

Like IQ for example. The standard deviation is 15 points. So if your IQ is 130, you are "2 standard deviations from the norm".

But is there a % formula to calculate percentile? I think there is but I can't remember it. And are these %'s the same for everything?

I seem to remember seeing it was like 69%-95%-99% or something?

[LetYouDown]

I believe you're referring to confidence intervals with the numbers you cited. These should be the exact numbers.

0.6826895
0.9544997
0.9973002
0.9999366
0.9999994

Until someone comes along with enough time to explain it in layman's terms...here's a pretty thorough explanation:

http://mathworld.wolfram.com/StandardDeviation.html

With a semi-pre-requisite of:

http://mathworld.wolfram.com/Variance.html

[Cased Heel]

Yes that is what I was referring to. I only got as high as Pre-Cal Honors in HS, so I can't do that math, but I'm assuming

CI's are constant for any event?
And that the event itself defines what it's standard deviation is? For instance, since 68% of people's IQ score falls between 85-115, then 15 is determined as the standard deviation, right?

Thanks for the help.

[LetYouDown]

Sounds right to me. The majority of the math on those pages is really quite simple, once you figure out what the hell they're actually talking about. It would greatly help if they would just state what the equation represents in English. I read one of their articles once that had this ridiculously bizarre equation and I sat there and broke it all down only to figure out 15 minutes later that it was just calculating the mean.

[probman]

[ QUOTE ]

For instance, since 68% of people's IQ score falls between 85-115, then 15 is determined as the standard deviation, right?


[/ QUOTE ]

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.