statistics: stdev() Crashes on NaN, variance() Doesn't (tested)

A stray NaN in numeric data usually propagates quietly through arithmetic -- any operation touching it just produces another NaN. We measured whether Python's statistics module follows that pattern consistently across its variance-family functions, and it doesn't.

1. variance() propagates NaN cleanly; stdev() on the same data raises AttributeError

import statistics as st

nan = float("nan")
data = [1, 2, nan, 4]

print(st.variance(data))
print(st.stdev(data))

nan
Traceback (most recent call last):
  ...
  File ".../statistics.py", line 1211, in stdev
    return _float_sqrt_of_frac(mss.numerator, mss.denominator)
                               ^^^^^^^^^^^^^
AttributeError: 'float' object has no attribute 'numerator'

Measured: variance() on data containing a NaN returns nan -- the expected, quiet propagation. stdev() on the exact same list doesn't return nan; it raises AttributeError from deep inside the module's internals. stdev() computes variance as an exact Fraction internally and expects a .numerator attribute to take the square root precisely, but a NaN in the input collapses that internal value to a plain float, which has no such attribute -- the exception leaks an implementation detail instead of surfacing as a clean, catchable error.

2. The population variants have the exact same split

import statistics as st

nan = float("nan")
data = [1, 2, nan, 4]

print(st.pvariance(data))
print(st.pstdev(data))

nan
Traceback (most recent call last):
  ...
AttributeError: 'float' object has no attribute 'numerator'

Measured: pvariance() (population variance) also returns nan cleanly, while pstdev() raises the identical AttributeError as stdev(). The split is consistent across both the sample and population variants: the two functions that return variance directly handle NaN fine; the two that take a square root of it don't.

3. Position and list size don't matter -- any NaN anywhere triggers it

import statistics as st

nan = float("nan")

try:
    st.stdev([nan, 1, 2, 4])
except AttributeError as e:
    print("leading nan:", e)

try:
    st.stdev([1] * 100 + [nan])
except AttributeError as e:
    print("trailing nan in 101 values:", e)

leading nan: 'float' object has no attribute 'numerator'
trailing nan in 101 values: 'float' object has no attribute 'numerator'

Measured: the crash happens regardless of where the NaN sits in the list or how many other values surround it -- a single NaN anywhere is enough. Code that checks for bad data by catching StatisticsError around a stdev() call (the module's documented exception type) won't catch this -- AttributeError is a different exception class entirely, so the except clause silently lets it through as an unhandled crash.

Written with AI assistance. Measured on 2026-10-04 with Python 3.13.5's built-in statistics module: called variance(), stdev(), pvariance(), and pstdev() on the same data containing a float('nan') value. PlainHeaders is our extension; Python's statistics module is built in.