From 99a5137bdb1f760a3bdd16266e09c6d657dd7dae Mon Sep 17 00:00:00 2001
From: Matthew Roeschke <10647082+mroeschke@users.noreply.github.com>
Date: Tue, 18 Apr 2023 11:56:55 -0700
Subject: [PATCH] BUG: ArrowExtensionArray returning approximate median

---
 doc/source/whatsnew/v2.0.1.rst       | 1 +
 pandas/core/arrays/arrow/array.py    | 8 +++++++-
 pandas/tests/extension/test_arrow.py | 6 ++++++
 3 files changed, 14 insertions(+), 1 deletion(-)

diff --git a/doc/source/whatsnew/v2.0.1.rst b/doc/source/whatsnew/v2.0.1.rst
index 9c867544a324b..89d15115197f7 100644
--- a/doc/source/whatsnew/v2.0.1.rst
+++ b/doc/source/whatsnew/v2.0.1.rst
@@ -26,6 +26,7 @@ Bug fixes
 ~~~~~~~~~
 - Bug in :attr:`Series.dt.days` that would overflow ``int32`` number of days (:issue:`52391`)
 - Bug in :class:`arrays.DatetimeArray` constructor returning an incorrect unit when passed a non-nanosecond numpy datetime array (:issue:`52555`)
+- Bug in :func:`Series.median` with :class:`ArrowDtype` returning an approximate median (:issue:`52679`)
 - Bug in :func:`pandas.testing.assert_series_equal` where ``check_dtype=False`` would still raise for datetime or timedelta types with different resolutions (:issue:`52449`)
 - Bug in :func:`read_csv` casting PyArrow datetimes to NumPy when ``dtype_backend="pyarrow"`` and ``parse_dates`` is set causing a performance bottleneck in the process (:issue:`52546`)
 - Bug in :func:`to_datetime` and :func:`to_timedelta` when trying to convert numeric data with a :class:`ArrowDtype` (:issue:`52425`)
diff --git a/pandas/core/arrays/arrow/array.py b/pandas/core/arrays/arrow/array.py
index b60d29aff6991..ef6f4601ed074 100644
--- a/pandas/core/arrays/arrow/array.py
+++ b/pandas/core/arrays/arrow/array.py
@@ -1270,7 +1270,7 @@ def pyarrow_meth(data, skip_nulls, **kwargs):
 
         else:
             pyarrow_name = {
-                "median": "approximate_median",
+                "median": "quantile",
                 "prod": "product",
                 "std": "stddev",
                 "var": "variance",
@@ -1286,6 +1286,9 @@ def pyarrow_meth(data, skip_nulls, **kwargs):
         # GH51624: pyarrow defaults to min_count=1, pandas behavior is min_count=0
         if name in ["any", "all"] and "min_count" not in kwargs:
             kwargs["min_count"] = 0
+        elif name == "median":
+            # GH 52679: Use quantile instead of approximate_median
+            kwargs["q"] = 0.5
 
         try:
             result = pyarrow_meth(data_to_reduce, skip_nulls=skipna, **kwargs)
@@ -1297,6 +1300,9 @@ def pyarrow_meth(data, skip_nulls, **kwargs):
                 f"upgrading pyarrow."
             )
             raise TypeError(msg) from err
+        if name == "median":
+            # GH 52679: Use quantile instead of approximate_median; returns array
+            result = result[0]
         if pc.is_null(result).as_py():
             return self.dtype.na_value
 
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index 7e4532b1ee326..45b973a44e56d 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -504,6 +504,12 @@ def test_reduce_series(self, data, all_numeric_reductions, skipna, request):
             request.node.add_marker(xfail_mark)
         super().test_reduce_series(data, all_numeric_reductions, skipna)
 
+    @pytest.mark.parametrize("typ", ["int64", "uint64", "float64"])
+    def test_median_not_approximate(self, typ):
+        # GH 52679
+        result = pd.Series([1, 2], dtype=f"{typ}[pyarrow]").median()
+        assert result == 1.5
+
 
 class TestBaseBooleanReduce(base.BaseBooleanReduceTests):
     @pytest.mark.parametrize("skipna", [True, False])