File: statistics.mpi

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Mean(x) := Add(x)/Length(x);

GeometricMean(x) := Factorize(x)^(1/Length(x));

Median(x) :=
[
 Local(sx,n,n2); // s[orted]x
 sx := BubbleSort(x,"<");
 n := Length(x);
 n2 := (n>>1);
 If(Mod(n,2) = 1, sx[n2+1], (sx[n2]+sx[n2+1])/2);
];

Variance(x) := Add((x-Mean(x))^2)/Length(x);
UnbiasedVariance(x) := Add((x-Mean(x))^2)/(Length(x)-1);

// stdev in Wester benchmark
StandardDeviation(x) := Sqrt(UnbiasedVariance(x)); 
// Why Sqrt(1.01) --> Sqrt(1.01) ?