Summarize data in Haskell

Use HMath.Statistics for basic descriptive statistics over finite, nonempty lists. These legacy pure functions return a number directly and raise a pure error on an empty list. Validate that precondition before calling. The Python binding currently exposes tensor reductions rather than these APIs.

Compute a population summary

import qualified HMath.Statistics as Statistics

main :: IO ()
main = do
    let samples = [1, 3 :: Double]
    if null samples then fail "A summary needs at least one observation" else pure ()
    if Statistics.mean samples == 2
        && Statistics.variance samples == 1
        && Statistics.standardDeviation samples == 1
        && Statistics.median samples == 2
        then putStrLn "mean=2, population variance=1, median=2"
        else fail "Unexpected summary"

The expected output is mean=2, population variance=1, median=2. These particular results are exactly representable; general floating-point data needs approximate comparison.

Interpret the denominator

variance computes population variance:

\[ \mu=\frac{1}{n}\sum_{i=1}^{n}x_i,\qquad \mathrm{variance}(x)=\frac{1}{n}\sum_{i=1}^{n}(x_i-\mu)^2. \]

It divides by \(n\), not \(n-1\). Do not label this result an unbiased sample variance. standardDeviation is the square root of that population variance. For even-length input, median averages the two central sorted values.

These generic functions do not provide a universal overflow or numerical stability guarantee. Use the Statistics API for signatures and numerical conventions for interpreting finite arithmetic and error behavior.