GH-77265: Document NaN handling in statistics functions that sort or count (GH-94676) (#94726)

Author: miss-islington

Doc/library/statistics.rst

@@ -35,6 +35,35 @@ and implementation-dependent.  If your input data consists of mixed types,
 you may be able to use :func:`map` to ensure a consistent result, for
 example: ``map(float, input_data)``.
 
+Some datasets use ``NaN`` (not a number) values to represent missing data.
+Since NaNs have unusual comparison semantics, they cause surprising or
+undefined behaviors in the statistics functions that sort data or that count
+occurrences.  The functions affected are ``median()``, ``median_low()``,
+``median_high()``, ``median_grouped()``, ``mode()``, ``multimode()``, and
+``quantiles()``.  The ``NaN`` values should be stripped before calling these
+functions::
+
+    >>> from statistics import median
+    >>> from math import isnan
+    >>> from itertools import filterfalse
+
+    >>> data = [20.7, float('NaN'),19.2, 18.3, float('NaN'), 14.4]
+    >>> sorted(data)  # This has surprising behavior
+    [20.7, nan, 14.4, 18.3, 19.2, nan]
+    >>> median(data)  # This result is unexpected
+    16.35
+
+    >>> sum(map(isnan, data))    # Number of missing values
+    2
+    >>> clean = list(filterfalse(isnan, data))  # Strip NaN values
+    >>> clean
+    [20.7, 19.2, 18.3, 14.4]
+    >>> sorted(clean)  # Sorting now works as expected
+    [14.4, 18.3, 19.2, 20.7]
+    >>> median(clean)       # This result is now well defined
+    18.75
+
+
 Averages and measures of central location
 -----------------------------------------