statistics.pstdev overflows for large finite values when given the correct mean

[augusto-rehfeldt]

Bug report

Bug description:

Documented behaviour: The pvariance docstring, incorporated by pstdev's sentence "See pvariance for arguments and other details", states: "The optional argument mu, if given, should be the mean of the data. If it is missing or None, the mean is automatically calculated." pstdev promises: "Return the square root of the population variance."

Expected: pstdev([-1e160, 1e160], mu=0.0) returns approximately 1e160, agreeing with the call without mu.

Actual: Raises ValueError: inf or nan encountered in data.

import math
import statistics

a = 1e160
data, mu = [-a, a], 0.0
expected = math.hypot(*data) / math.sqrt(len(data))
if not (all(map(math.isfinite, data)) and math.fsum(data) / len(data) == mu):
    print("REFUTATION REJECTED: invalid input or incorrect mean")
else:
    try:
        actual = statistics.pstdev(data, mu=mu)
    except Exception as e:
        actual = f"{type(e).__name__}: {e}"
    if not isinstance(actual, float) or not math.isclose(actual, expected, rel_tol=1e-15):
        print("REFUTATION CONFIRMED:", {"data": data, "mu": mu},
              "actual=", actual, "expected=", expected)
    else:
        print("REFUTATION REJECTED: result agrees with documented expectation")

Output on Python 3.14.6 (Windows-11-10.0.26220-SP0), standard library statistics:

REFUTATION CONFIRMED: {'data': [-1e+160, 1e+160], 'mu': 0.0} actual= ValueError: inf or nan encountered in data expected= 1e+160

This report was found and written by an automated property-testing tool I run (bugforge). The reproducer above was executed and its output is pasted unedited; no person reviewed the report before it was filed. The search script is in https://github.com/augusto-rehfeldt/bugforge-results/tree/main/statistics-20261003-081656-c2

CPython versions tested on:

3.14

Operating systems tested on:

Windows

[ZeroIntensity]

See #158748 (comment).