Variance

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

Sample variance of a collection of numbers.

✓ checked against that system · ! checked, with disagreements (hover a chip)Wolfram LanguageVariance✓↗

Variance((collection<any> | distribution | number)+) -> nan | real<0..>Sample variance of a collection of numbers.

SageMathvariance(collection<any> | distribution | number)

Typed signatures

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

Domain: Compute engine

Examples

Scope #

The sample variance of 1 to 4 is $\frac53$

live ↗

In$\mathrm{Variance}(\bigl\lbrack1, 2, 3, 4\bigr\rbrack)$Out$\frac{5}{3}$

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

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In$\mathrm{Variance}(N(\bigl\lbrack1, 2, 3, 4\bigr\rbrack, 30))$Out$1.666\,666\,666\,666\,666\,666\,67$

An unbound data symbol keeps the result symbolic

live ↗

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

For a binomial it is $np(1-p)$

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

A Cauchy-like density is left unevaluated

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

Applications #

N cannot evaluate a symbolic dataset, so both entries stay

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In$N(\bigl\lbrack\mathrm{mean}(\mathrm{data}), \mathrm{Variance}(\mathrm{data})\bigr\rbrack)$Out$\bigl\lbrack\mathrm{mean}(\mathrm{data}), \mathrm{Variance}(\mathrm{data})\bigr\rbrack$

Likewise a symbolic dataset stays unevaluated under N

live ↗

In$N(\mathrm{Variance}(\mathrm{heights}))$Out$\mathrm{Variance}(\mathrm{heights})$

About

Examples	7
Checked against	Wolfram Language 7 agreeSageMath 2 agree3 errorOscar 2 agree
Crosswalk	Wolfram LanguageSageMath

Implementation

mappedoscarpackages/oracle/src/mappings.ts

mappedsagepackages/oracle/src/mappings.ts