statistics.fmean raises OverflowError for finite inputs with a representable mean

[augusto-rehfeldt]

Bug report

Bug description:

Documented behaviour: "Convert data to floats and compute the arithmetic mean." — statistics.fmean docstring.

Expected: Return approximately 1e308 without raising.

Actual: OverflowError: intermediate overflow in fsum

import statistics, math
from fractions import Fraction

data = [1e308, 1e308]
if not data or not all(isinstance(x, float) and math.isfinite(x) for x in data):
    print("REFUTATION REJECTED: input is not nonempty finite float data")
else:
    expected = float(sum(map(Fraction, data), Fraction()) / len(data))
    try:
        actual = statistics.fmean(data)
        broken = not math.isclose(actual, expected, rel_tol=1e-15)
    except Exception as e:
        actual = f"{type(e).__name__}: {e}"
        broken = True
    if broken:
        print(f"REFUTATION CONFIRMED: input={data!r}, actual={actual!r}, expected={expected!r}")
    else:
        print("REFUTATION REJECTED: result matches the independently computed arithmetic mean")

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

REFUTATION CONFIRMED: input=[1e+308, 1e+308], actual='OverflowError: intermediate overflow in fsum', expected=1e+308

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-20261003-124541-c1

CPython versions tested on:

3.14

Operating systems tested on:

Windows

[ZeroIntensity]

See #158748 (comment).