gh-110150: Fix base case handling in quantiles()

Doc/library/statistics.rst

@@ -585,7 +585,7 @@ However, for reading convenience, most of the examples show sorted sequences.
 
    The *data* can be any iterable containing sample data.  For meaningful
    results, the number of data points in *data* should be larger than *n*.
-   Raises :exc:`StatisticsError` if there are not at least two data points.
+   Raises :exc:`StatisticsError` if there is not at least one data point.
 
    The cut points are linearly interpolated from the
    two nearest data points.  For example, if a cut point falls one-third
@@ -625,6 +625,11 @@ However, for reading convenience, most of the examples show sorted sequences.
 
    .. versionadded:: 3.8
 
+   .. versionchanged:: 3.13
+      No longer raises an exception for an input with only a single data point.
+      This allows quantile estimates to be built up one sample point
+      at a time becoming gradually more refined with each new data point.
+
 .. function:: covariance(x, y, /)
 
    Return the sample covariance of two inputs *x* and *y*. Covariance

Lib/statistics.py

@@ -844,7 +844,9 @@ def quantiles(data, *, n=4, method='exclusive'):
     data = sorted(data)
     ld = len(data)
     if ld < 2:
-        raise StatisticsError('must have at least two data points')
+        if ld == 1:
+            return data * (n - 1)
+        raise StatisticsError('must have at least one data point')
     if method == 'inclusive':
         m = ld - 1
         result = []

Lib/test/test_statistics.py

@@ -2454,6 +2454,11 @@ def f(x):
             data = random.choices(range(100), k=k)
             q1, q2, q3 = quantiles(data, method='inclusive')
             self.assertEqual(q2, statistics.median(data))
+        # Base case with a single data point:  When estimating quantiles from
+        # a sample, we want to be able to add one sample point at a time,
+        # getting increasingly better estimates.
+        self.assertEqual(quantiles([10], n=4), [10.0, 10.0, 10.0])
+        self.assertEqual(quantiles([10], n=4, method='exclusive'), [10.0, 10.0, 10.0])
 
     def test_equal_inputs(self):
         quantiles = statistics.quantiles
@@ -2504,7 +2509,7 @@ def test_error_cases(self):
         with self.assertRaises(ValueError):
             quantiles([10, 20, 30], method='X') # method is unknown
         with self.assertRaises(StatisticsError):
-            quantiles([10], n=4)                # not enough data points
+            quantiles([], n=4)                  # not enough data points
         with self.assertRaises(TypeError):
             quantiles([10, None, 30], n=4)      # data is non-numeric
 

Misc/NEWS.d/next/Library/2023-09-30-12-50-47.gh-issue-110150.9j0Ij5.rst

@@ -0,0 +1,2 @@
+Fix base case handling in statistics.quantiles.  Now allows a single data
+point.