diff --git a/pandas/core/nanops.py b/pandas/core/nanops.py
index 88662a4fabed8..356c54e80f0ca 100644
--- a/pandas/core/nanops.py
+++ b/pandas/core/nanops.py
@@ -685,7 +685,7 @@ def get_median(x):
             values = values.astype("f8")
         except ValueError as err:
             # e.g. "could not convert string to float: 'a'"
-            raise TypeError from err
+            raise TypeError(str(err)) from err
         if mask is not None:
             values[mask] = np.nan
 
diff --git a/pandas/tests/reductions/test_reductions.py b/pandas/tests/reductions/test_reductions.py
index 8c2297699807d..473e836be8e50 100644
--- a/pandas/tests/reductions/test_reductions.py
+++ b/pandas/tests/reductions/test_reductions.py
@@ -526,9 +526,17 @@ def test_numpy_minmax_period(self):
     def test_min_max_categorical(self):
 
         ci = pd.CategoricalIndex(list("aabbca"), categories=list("cab"), ordered=False)
-        with pytest.raises(TypeError):
+        msg = (
+            r"Categorical is not ordered for operation min\n"
+            r"you can use .as_ordered\(\) to change the Categorical to an ordered one\n"
+        )
+        with pytest.raises(TypeError, match=msg):
             ci.min()
-        with pytest.raises(TypeError):
+        msg = (
+            r"Categorical is not ordered for operation max\n"
+            r"you can use .as_ordered\(\) to change the Categorical to an ordered one\n"
+        )
+        with pytest.raises(TypeError, match=msg):
             ci.max()
 
         ci = pd.CategoricalIndex(list("aabbca"), categories=list("cab"), ordered=True)
@@ -880,16 +888,20 @@ def test_all_any_params(self):
         tm.assert_series_equal(s.all(level=0), Series([False, True, False]))
         tm.assert_series_equal(s.any(level=0), Series([False, True, True]))
 
-        # bool_only is not implemented with level option.
-        with pytest.raises(NotImplementedError):
+        msg = "Option bool_only is not implemented with option level"
+        with pytest.raises(NotImplementedError, match=msg):
             s.any(bool_only=True, level=0)
-        with pytest.raises(NotImplementedError):
+        with pytest.raises(NotImplementedError, match=msg):
             s.all(bool_only=True, level=0)
 
         # bool_only is not implemented alone.
-        with pytest.raises(NotImplementedError):
+        # TODO GH38810 change this error message to:
+        # "Series.any does not implement bool_only"
+        msg = "Series.any does not implement numeric_only"
+        with pytest.raises(NotImplementedError, match=msg):
             s.any(bool_only=True)
-        with pytest.raises(NotImplementedError):
+        msg = "Series.all does not implement numeric_only."
+        with pytest.raises(NotImplementedError, match=msg):
             s.all(bool_only=True)
 
     def test_all_any_boolean(self):
@@ -980,13 +992,21 @@ def test_assert_idxminmax_raises(self, test_input, error_type):
         """
         Cases where ``Series.argmax`` and related should raise an exception
         """
-        with pytest.raises(error_type):
+        msg = (
+            "reduction operation 'argmin' not allowed for this dtype|"
+            "attempt to get argmin of an empty sequence"
+        )
+        with pytest.raises(error_type, match=msg):
             test_input.idxmin()
-        with pytest.raises(error_type):
+        with pytest.raises(error_type, match=msg):
             test_input.idxmin(skipna=False)
-        with pytest.raises(error_type):
+        msg = (
+            "reduction operation 'argmax' not allowed for this dtype|"
+            "attempt to get argmax of an empty sequence"
+        )
+        with pytest.raises(error_type, match=msg):
             test_input.idxmax()
-        with pytest.raises(error_type):
+        with pytest.raises(error_type, match=msg):
             test_input.idxmax(skipna=False)
 
     def test_idxminmax_with_inf(self):
diff --git a/pandas/tests/reductions/test_stat_reductions.py b/pandas/tests/reductions/test_stat_reductions.py
index 67e871f8b67c2..ab13893901104 100644
--- a/pandas/tests/reductions/test_stat_reductions.py
+++ b/pandas/tests/reductions/test_stat_reductions.py
@@ -98,7 +98,8 @@ def _check_stat_op(
             # mean, idxmax, idxmin, min, and max are valid for dates
             if name not in ["max", "min", "mean", "median", "std"]:
                 ds = Series(pd.date_range("1/1/2001", periods=10))
-                with pytest.raises(TypeError):
+                msg = f"'DatetimeArray' does not implement reduction '{name}'"
+                with pytest.raises(TypeError, match=msg):
                     f(ds)
 
             # skipna or no
@@ -134,11 +135,12 @@ def _check_stat_op(
 
             # check on string data
             if name not in ["sum", "min", "max"]:
-                with pytest.raises(TypeError):
+                with pytest.raises(TypeError, match=None):
                     f(Series(list("abc")))
 
             # Invalid axis.
-            with pytest.raises(ValueError):
+            msg = "No axis named 1 for object type Series"
+            with pytest.raises(ValueError, match=msg):
                 f(string_series_, axis=1)
 
             # Unimplemented numeric_only parameter.