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Re: Definitions missing
Posted:
Jun 5, 2013 3:15 AM


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@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/(n1)? > > 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 > >



