StandardDeviation

Generated from the engine's own definition: compute-engine's symbol, which we neither extend nor document by hand.

Sample Standard Deviation of a collection of numbers.

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StandardDeviation((collection<any> | distribution | number)+) -> nan | real<0..>as compute-engine declares it

SageMathstd(collection<any> | distribution | number)

Typed signatures

Type	Package	Applies
((collection<nothing | number> | distribution | number)+) -> nan | real<0..>	compute-engine	always

Domain: Compute engine

Examples

Scope #

A sample standard deviation, $\sqrt{15}/3 = \sqrt{5/3}$

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In$\mathrm{StandardDeviation}(\bigl\lbrack1, 2, 3, 4\bigr\rbrack)$Out$\frac{\sqrt{15}}{3}$

A 30-digit numeric list gives a 30-digit result

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In$\mathrm{StandardDeviation}(N(\bigl\lbrack1, 2, 3, 4\bigr\rbrack, 30))$Out$1.290\,994\,448\,735\,805\,628\,39$

With an undefined list the result stays symbolic

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In$N(\mathrm{StandardDeviation}(\mathrm{ts}))$Out$\mathrm{StandardDeviation}(\mathrm{ts})$

For a binomial it is $\sqrt{np(1-p)}$

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In$\mathrm{StandardDeviation}(\operatorname{BinomialDistribution}(n, p))$Out$\sqrt{np×(1-p)}$

A custom Cauchy-like density is left symbolic

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In$\mathrm{StandardDeviation}(\mathrm{ProbabilityDistribution}(\frac{\sqrt{2}}{π((x-2)^4+1)}, \bigl\lbrack x, -∞, ∞\bigr\rbrack))$Out$\mathrm{StandardDeviation}(\mathrm{ProbabilityDistribution}(\frac{\sqrt{2}}{π(x-2)^4+π}, \bigl\lbrack x, -∞, ∞\bigr\rbrack))$

About

Examples	5
Checked against	Wolfram Language 5 agreeSageMath 2 agree1 error
Crosswalk	Wolfram LanguageSageMath

Implementation

mappedsagepackages/oracle/src/mappings.ts