Bug fix - GroupBy.describe produces inconsistent results for empty datasets

doc/source/whatsnew/v1.5.0.rst

@@ -786,6 +786,8 @@ Groupby/resample/rolling
 - Bug in :meth:`.Rolling.var` would segfault calculating weighted variance when window size was larger than data size (:issue:`46760`)
 - Bug in :meth:`Grouper.__repr__` where ``dropna`` was not included. Now it is (:issue:`46754`)
 - Bug in :meth:`DataFrame.rolling` gives ValueError when center=True, axis=1 and win_type is specified (:issue:`46135`)
+- Bug in :meth:`.DataFrameGroupBy.describe` and :meth:`.SeriesGroupBy.describe` produces inconsistent results for empty datasets (:issue:`41575`)
+-
 
 Reshaping
 ^^^^^^^^^

pandas/core/groupby/groupby.py

@@ -2542,6 +2542,14 @@ def ohlc(self) -> DataFrame:
     @doc(DataFrame.describe)
     def describe(self, **kwargs):
         with self._group_selection_context():
+            if len(self._selected_obj) == 0:
+                described = self._selected_obj.describe(**kwargs)
+                if self._selected_obj.ndim == 1:
+                    result = described
+                else:
+                    result = described.unstack()
+                return result.to_frame().T.iloc[:0]
+
             result = self._python_apply_general(
                 lambda x: x.describe(**kwargs),
                 self._selected_obj,

pandas/tests/groupby/test_function.py

@@ -1354,3 +1354,28 @@ def test_deprecate_numeric_only(
         # Doesn't have numeric_only argument and fails on nuisance columns
         with pytest.raises(TypeError, match=r"unsupported operand type"):
             method(*args, **kwargs)
+
+
+@pytest.mark.parametrize("dtype", [int, float, object])
+@pytest.mark.parametrize(
+    "kwargs",
+    [
+        {"percentiles": [0.10, 0.20, 0.30], "include": "all", "exclude": None},
+        {"percentiles": [0.10, 0.20, 0.30], "include": None, "exclude": ["int"]},
+        {"percentiles": [0.10, 0.20, 0.30], "include": ["int"], "exclude": None},
+    ],
+)
+def test_groupby_empty_dataset(dtype, kwargs):
+    # GH#41575
+    df = DataFrame([[1, 2, 3]], columns=["A", "B", "C"], dtype=dtype)
+    df["B"] = df["B"].astype(int)
+    df["C"] = df["C"].astype(float)
+
+    result = df.iloc[:0].groupby("A").describe(**kwargs)
+    expected = df.groupby("A").describe(**kwargs).reset_index(drop=True).iloc[:0]
+    tm.assert_frame_equal(result, expected)
+
+    result = df.iloc[:0].groupby("A").B.describe(**kwargs)
+    expected = df.groupby("A").B.describe(**kwargs).reset_index(drop=True).iloc[:0]
+    expected.index = Index([])
+    tm.assert_frame_equal(result, expected)