`statistics.stdev()` raises `AttributeError` when data contains infinity

[T90REAL]

Bug report

Bug description:

statistics.stdev() crashes when processing data containing inf, while statistics.variance() handles the same input correctly. This violates the invariant stdev = sqrt(variance).

import statistics

data = [1.0, 2.0, float('inf'), 4.0, 5.0]

# Works fine
print(statistics.variance(data))  # Returns: inf

# Crashes
statistics.stdev(data) # AttributeError: 'float' object has no attribute 'numerator'

inf
Traceback (most recent call last):
  File "/data/src/test.py", line 9, in <module>
    statistics.stdev(data) # AttributeError: 'float' object has no attribute 'numerator'
    ^^^^^^^^^^^^^^^^^^^^^^
  File "/home/py312/lib/python3.12/statistics.py", line 974, in stdev
    return _float_sqrt_of_frac(mss.numerator, mss.denominator)
                               ^^^^^^^^^^^^^
AttributeError: 'float' object has no attribute 'numerator'

Expected: stdev(data) should return inf (since sqrt(variance) = sqrt(inf) = inf)

CPython versions tested on:

3.12

Operating systems tested on:

Linux

[picnixz]

I'm not sure statistics.variance is even remotely correct here. For instance, if we consider the mean of the sample as simply being the averaged sum, it would be $\infty$. So, statistics.variance(data, float('inf')) == statistics.variance(data), which is not the case. The first one gives nan while the second returns $\infty$ but the second argument is meant to be the known mean, so we already have inconsistencies.

@rhettinger Was statistics ever meant to handle infinite values in data points? I see that geometric_mean handles NaN inputs but that's the only function that does so.

[skirpichev]

Perhaps, just this:

diff --git a/Lib/statistics.py b/Lib/statistics.py
index 3d805cb0739..c01c2a945a2 100644
--- a/Lib/statistics.py
+++ b/Lib/statistics.py
@@ -621,7 +621,9 @@ def stdev(data, xbar=None):
     mss = ss / (n - 1)
     if issubclass(T, Decimal):
         return _decimal_sqrt_of_frac(mss.numerator, mss.denominator)
-    return _float_sqrt_of_frac(mss.numerator, mss.denominator)
+    elif issubclass(T, Fraction):
+        return _float_sqrt_of_frac(mss.numerator, mss.denominator)
+    return math.sqrt(mss)
 
 
 def pstdev(data, mu=None):

[T90REAL]

statistics.pstdev() also has this issue, and it could be solved in the same way.