bpo-36546: Add more tests and expand docs (#13406)

1 files changed, 27 insertions, 11 deletions

diff --git a/Lib/test/test_statistics.py b/Lib/test/test_statistics.py
index 1922de5..946c742 100644
--- a/Lib/test/test_statistics.py
+++ b/Lib/test/test_statistics.py
@@ -2161,17 +2161,18 @@ class TestQuantiles(unittest.TestCase):
             # Quantiles should be idempotent
             if len(expected) >= 2:
                 self.assertEqual(quantiles(expected, n=n), expected)
-            # Cross-check against other methods
-            if len(data) >= n:
-                # After end caps are added, method='inclusive' should
-                # give the same result as method='exclusive' whenever
-                # there are more data points than desired cut points.
-                padded_data = [min(data) - 1000] + data + [max(data) + 1000]
-                self.assertEqual(
-                    quantiles(data, n=n),
-                    quantiles(padded_data, n=n, method='inclusive'),
-                    (n, data),
-                )
+            # Cross-check against method='inclusive' which should give
+            # the same result after adding in minimum and maximum values
+            # extrapolated from the two lowest and two highest points.
+            sdata = sorted(data)
+            lo = 2 * sdata[0] - sdata[1]
+            hi = 2 * sdata[-1] - sdata[-2]
+            padded_data = data + [lo, hi]
+            self.assertEqual(
+                quantiles(data, n=n),
+                quantiles(padded_data, n=n, method='inclusive'),
+                (n, data),
+            )
             # Invariant under tranlation and scaling
             def f(x):
                 return 3.5 * x - 1234.675
@@ -2188,6 +2189,11 @@ class TestQuantiles(unittest.TestCase):
             actual = quantiles(statistics.NormalDist(), n=n)
             self.assertTrue(all(math.isclose(e, a, abs_tol=0.0001)
                             for e, a in zip(expected, actual)))
+        # Q2 agrees with median()
+        for k in range(2, 60):
+            data = random.choices(range(100), k=k)
+            q1, q2, q3 = quantiles(data)
+            self.assertEqual(q2, statistics.median(data))
 
     def test_specific_cases_inclusive(self):
         # Match results computed by hand and cross-checked
@@ -2233,6 +2239,11 @@ class TestQuantiles(unittest.TestCase):
             actual = quantiles(statistics.NormalDist(), n=n, method="inclusive")
             self.assertTrue(all(math.isclose(e, a, abs_tol=0.0001)
                             for e, a in zip(expected, actual)))
+        # Natural deciles
+        self.assertEqual(quantiles([0, 100], n=10, method='inclusive'),
+                         [10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 70.0, 80.0, 90.0])
+        self.assertEqual(quantiles(range(0, 101), n=10, method='inclusive'),
+                         [10.0, 20.0, 30.0, 40.0, 50.0, 60.0, 70.0, 80.0, 90.0])
         # Whenever n is smaller than the number of data points, running
         # method='inclusive' should give the same result as method='exclusive'
         # after the two included extreme points are removed.
@@ -2242,6 +2253,11 @@ class TestQuantiles(unittest.TestCase):
         data.remove(max(data))
         expected = quantiles(data, n=32)
         self.assertEqual(expected, actual)
+        # Q2 agrees with median()
+        for k in range(2, 60):
+            data = random.choices(range(100), k=k)
+            q1, q2, q3 = quantiles(data, method='inclusive')
+            self.assertEqual(q2, statistics.median(data))
 
     def test_equal_inputs(self):
         quantiles = statistics.quantiles