Wolfram Language Fast Introduction for Math Students
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Statistics

In the Wolfram Language, statistical functions accept either lists or symbolic distributions as an argument.

Compute the mean of a list of numbers:

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⨯ 
Mean[{1, 2, 4, 5}]
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Find the correlation of multiple lists:

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⨯ 
Correlation[{1, 3, 5}, {6, 4, 2}]
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Find the standard deviation of a Poisson distribution:

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⨯ 
StandardDeviation[PoissonDistribution[2]]
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Calculate the moment of a list of symbols:

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⨯ 
Moment[{x, y, z}, 2]
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Get the moment-generating function for a distribution:

(Type ESCmESC for μ and ESCsESC for σ.)
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⨯ 
MomentGeneratingFunction[NormalDistribution[\[Mu], \[Sigma]], t]
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Generate statistical data with RandomVariate:

(Use //Short to get a short summary of output.)
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⨯ 
RandomVariate[NormalDistribution[0, 1], {500, 2}] // Short
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Visualize the resulting data:

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⨯ 
Histogram3D[%]
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QUICK REFERENCE: Statistical Moments and Generating Functions »

QUICK REFERENCE: Statistical Visualization »