Re: Definitions missing

*To*: mathgroup at smc.vnet.net*Subject*: [mg131034] Re: Definitions missing*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Wed, 5 Jun 2013 03:28:21 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net*References*: <20130604060024.165FA6A67@smc.vnet.net>

To see how it is calculated just give it some symbolic data: len = 5; data = Array[d, len]; mean = Mean[data]; $Assumptions = {Element[data, Reals]}; (* used with Simplify *) s = StandardDeviation[data] // Simplify; s == Sqrt[Total[(data - mean)^2]/(len - 1)] // Simplify True Also, read all of the provided documentation. After pressing F1, Under "Tutorials" there is a link to "Basic Statistics" that gives the detailed definition for variance and defines standard deviation as the Sqrt of variance. Under "Properties and Relations"; there are five different ways shown for calculating the standard deviation of data: "StandardDeviation is a scaled Norm of deviations from the Mean" s == Norm[data - mean]/Sqrt[len - 1] // Simplify True "StandardDeviation is the square root of a scaled CentralMoment" s == Sqrt[CentralMoment[data, 2] len/(len - 1)] // Simplify True "StandardDeviation is a scaled RootMeanSquare of the deviations" s == RootMeanSquare[data - mean] Sqrt[len/(len - 1)] // Simplify True "StandardDeviation is the square root of a scaled Mean of squared deviations" s == Sqrt[Mean[(data - mean)^2] len/(len - 1)] // Simplify True "StandardDeviation as a scaled EuclideanDistance from the Mean" s == EuclideanDistance[data, Table[mean, {len}]]/ Sqrt[(len - 1)] // Simplify True Bob Hanlon On Tue, Jun 4, 2013 at 2:00 AM, Dr. Wolfgang Hintze <weh at snafu.de> wrote: > I'm sometimes missing a short path to the *definition* of a > Mathematica function. Perhaps somebody here could give me a hint. > > Example: StandardDeviation > > I'm double clicking the keyword in the notebook, press F1 and arrive > in the help browser which tells me that "StandardDeviation" is the > standard deviation. > Fine, I almost expected that. But now, how is this quantity defined? > This is a simple example, of course, but I admit that I forget > sometimes if it was the sum of the cuadratic differences or the square > root of it, was it 1/n or 1/(n-1)? > > But the same holds for all functions which frequently are defined e.g. > by power series or integrals. I personally would like to see this > definition in the help browser. > > Sorry again for the perhaps trivial question. > > Regards, > Wolfgang > >

**References**:**Definitions missing***From:*"Dr. Wolfgang Hintze" <weh@snafu.de>