diff --git a/Lib/statistics.py b/Lib/statistics.py
index 01ca6c51dafcaf..d8df4e324704c5 100644
--- a/Lib/statistics.py
+++ b/Lib/statistics.py
@@ -1217,7 +1217,13 @@ def quantiles(data, *, n=4, method='exclusive'):
             j = i * m // n                               # rescale i to m/n
             j = 1 if j < 1 else ld-1 if j > ld-1 else j  # clamp to 1 .. ld-1
             delta = i*m - j*n                            # exact integer math
-            interpolated = (data[j - 1] * (n - delta) + data[j] * delta) / n
+            # When the endpoints are equal or delta is zero, avoid
+            # the interpolation formula which can be off by 1 ULP
+            # due to floating-point rounding
+            if (data[j - 1] == data[j]) or not delta:
+                interpolated = float(data[j - 1])
+            else:
+                interpolated = (data[j - 1] * (n - delta) + data[j] * delta) / n
             result.append(interpolated)
         return result
 
diff --git a/Lib/test/test_statistics.py b/Lib/test/test_statistics.py
index 677a87b51b9192..551d40ef8c402c 100644
--- a/Lib/test/test_statistics.py
+++ b/Lib/test/test_statistics.py
@@ -2652,6 +2652,24 @@ def test_equal_inputs(self):
             self.assertEqual(quantiles(data, method='inclusive'),
                             [10.0, 10.0, 10.0])
 
+    def test_monotonic_with_duplicate_floats(self):
+        quantiles = statistics.quantiles
+        for x in (3.141592653589793,  # irrational-ish
+                  1/3,                # repeating binary fraction
+                  0.1,                # non-exact decimal
+                  2.0,                # exact power of two
+                  1e300,              # large magnitude
+                  1e-300,             # small magnitude
+                  float.fromhex('0x1.fffffffffffffp+1023'),  # near max float
+                  sys.float_info.min, # smallest normal
+                  ):
+            for n in range(2, 20):
+                result = quantiles([x, x], n=n, method='exclusive')
+                self.assertEqual(result, sorted(result),
+                                 msg=f'x={x}, n={n}')
+                self.assertTrue(all(v == x for v in result),
+                                msg=f'x={x}, n={n}')
+
     def test_equal_sized_groups(self):
         quantiles = statistics.quantiles
         total = 10_000
diff --git a/Misc/NEWS.d/next/Library/2026-05-23-23-14-26.gh-issue-150318.Utah1I.rst b/Misc/NEWS.d/next/Library/2026-05-23-23-14-26.gh-issue-150318.Utah1I.rst
new file mode 100644
index 00000000000000..6c0e2340132f7a
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2026-05-23-23-14-26.gh-issue-150318.Utah1I.rst
@@ -0,0 +1 @@
+Fix ``quantiles(method='exclusive')`` returning unsorted cut points for duplicate floats.