diff --git a/pandas-stubs/core/frame.pyi b/pandas-stubs/core/frame.pyi
index 3c5b2010b..df25e8b90 100644
--- a/pandas-stubs/core/frame.pyi
+++ b/pandas-stubs/core/frame.pyi
@@ -2344,30 +2344,66 @@ class DataFrame(NDFrame, OpsMixin, _GetItemHack):
         axis: Axis | None = ...,
         level: Level | None = None,
     ) -> Self: ...
+    @overload
     def max(
         self,
-        axis: Axis | None = 0,
+        axis: None,
+        skipna: _bool | None = True,
+        numeric_only: _bool = False,
+        **kwargs: Any,
+    ) -> Scalar: ...
+    @overload
+    def max(
+        self,
+        axis: Axis = 0,
         skipna: _bool | None = True,
         numeric_only: _bool = False,
         **kwargs: Any,
     ) -> Series: ...
+    @overload
     def mean(
         self,
-        axis: Axis | None = 0,
+        axis: None,
+        skipna: _bool | None = True,
+        numeric_only: _bool = False,
+        **kwargs: Any,
+    ) -> Scalar: ...
+    @overload
+    def mean(
+        self,
+        axis: Axis = 0,
         skipna: _bool | None = True,
         numeric_only: _bool = False,
         **kwargs: Any,
     ) -> Series: ...
+    @overload
     def median(
         self,
-        axis: Axis | None = 0,
+        axis: None,
+        skipna: _bool | None = True,
+        numeric_only: _bool = False,
+        **kwargs: Any,
+    ) -> Scalar: ...
+    @overload
+    def median(
+        self,
+        axis: Axis = 0,
         skipna: _bool | None = True,
         numeric_only: _bool = False,
         **kwargs: Any,
     ) -> Series: ...
+    @overload
     def min(
         self,
-        axis: Axis | None = 0,
+        axis: None,
+        skipna: _bool | None = True,
+        numeric_only: _bool = False,
+        **kwargs: Any,
+    ) -> Scalar: ...
+    @overload
+    def min(
+        self,
+        axis: Axis = 0,
         skipna: _bool | None = True,
         numeric_only: _bool = False,
         **kwargs: Any,
diff --git a/tests/series/test_series.py b/tests/series/test_series.py
index 4e34a712e..7b0cb0615 100644
--- a/tests/series/test_series.py
+++ b/tests/series/test_series.py
@@ -578,10 +578,14 @@ def test_types_cumsum() -> None:
 
 def test_types_min() -> None:
     s = pd.Series([1, 2, 3, np.nan])
-    s.min()
-    s.min(axis=0)
-    s.groupby(level=0).min()
-    s.min(skipna=False)
+    check(assert_type(s.min(), float), np.floating)
+    check(assert_type(s.min(axis=0), float), np.floating)
+    check(
+        assert_type(s.groupby(level=0).min(), "pd.Series[float]"),
+        pd.Series,
+        np.floating,
+    )
+    check(assert_type(s.min(skipna=False), float), np.floating)
 
 
 def test_types_max() -> None:
diff --git a/tests/test_frame.py b/tests/test_frame.py
index 521d4b896..0a8a33511 100644
--- a/tests/test_frame.py
+++ b/tests/test_frame.py
@@ -713,6 +713,7 @@ def test_types_mean() -> None:
     df = pd.DataFrame(data={"col1": [2, 1], "col2": [3, 4]})
     check(assert_type(df.mean(), pd.Series), pd.Series)
     check(assert_type(df.mean(axis=0), pd.Series), pd.Series)
+    check(assert_type(df.mean(axis=None), Scalar), np.floating)
     check(assert_type(df.groupby(level=0).mean(), pd.DataFrame), pd.DataFrame)
     check(
         assert_type(df.mean(axis=1, skipna=True, numeric_only=False), pd.Series),
@@ -724,6 +725,7 @@ def test_types_median() -> None:
     df = pd.DataFrame(data={"col1": [2, 1], "col2": [3, 4]})
     check(assert_type(df.median(), pd.Series), pd.Series)
     check(assert_type(df.median(axis=0), pd.Series), pd.Series)
+    check(assert_type(df.median(axis=None), Scalar), np.floating)
     check(assert_type(df.groupby(level=0).median(), pd.DataFrame), pd.DataFrame)
     check(
         assert_type(df.median(axis=1, skipna=True, numeric_only=False), pd.Series),
@@ -820,12 +822,14 @@ def test_types_min() -> None:
     df = pd.DataFrame(data={"col1": [2, 1], "col2": [3, 4]})
     check(assert_type(df.min(), pd.Series), pd.Series)
     check(assert_type(df.min(axis=0), pd.Series), pd.Series)
+    check(assert_type(df.min(axis=None), Scalar), np.integer)
 
 
 def test_types_max() -> None:
     df = pd.DataFrame(data={"col1": [2, 1], "col2": [3, 4]})
     check(assert_type(df.max(), pd.Series), pd.Series)
     check(assert_type(df.max(axis=0), pd.Series), pd.Series)
+    check(assert_type(df.max(axis=None), Scalar), np.integer)
 
 
 def test_types_quantile() -> None: