BUG (string dtype): fix qualifier in memory usage info

Author: jorisvandenbossche

pandas/core/indexes/base.py

@@ -5139,7 +5139,9 @@ def _is_memory_usage_qualified(self) -> bool:
         """
         Return a boolean if we need a qualified .info display.
         """
-        return is_object_dtype(self.dtype)
+        return is_object_dtype(self.dtype) or (
+            is_string_dtype(self.dtype) and self.dtype.storage == "python"
+        )
 
     def __contains__(self, key: Any) -> bool:
         """

pandas/core/indexes/multi.py

@@ -66,6 +66,7 @@
     is_list_like,
     is_object_dtype,
     is_scalar,
+    is_string_dtype,
     pandas_dtype,
 )
 from pandas.core.dtypes.dtypes import (
@@ -1425,10 +1426,12 @@ def dtype(self) -> np.dtype:
     def _is_memory_usage_qualified(self) -> bool:
         """return a boolean if we need a qualified .info display"""
 
-        def f(level) -> bool:
-            return "mixed" in level or "string" in level or "unicode" in level
+        def f(dtype) -> bool:
+            return is_object_dtype(dtype) or (
+                is_string_dtype(dtype) and dtype.storage == "python"
+            )
 
-        return any(f(level.inferred_type) for level in self.levels)
+        return any(f(level.dtype) for level in self.levels)
 
     # Cannot determine type of "memory_usage"
     @doc(Index.memory_usage)  # type: ignore[has-type]

pandas/tests/series/methods/test_info.py

@@ -7,10 +7,14 @@
 
 from pandas._config import using_string_dtype
 
-from pandas.compat import PYPY
+from pandas.compat import (
+    HAS_PYARROW,
+    PYPY,
+)
 
 from pandas import (
     CategoricalIndex,
+    Index,
     MultiIndex,
     Series,
     date_range,
@@ -142,14 +146,17 @@ def test_info_memory_usage_deep_pypy():
     assert s_object.memory_usage(deep=True) == s_object.memory_usage()
 
 
-@pytest.mark.xfail(using_string_dtype(), reason="TODO(infer_string)", strict=False)
 @pytest.mark.parametrize(
     "index, plus",
     [
         ([1, 2, 3], False),
-        (list("ABC"), True),
+        (Index(list("ABC"), dtype="str"), not (using_string_dtype() and HAS_PYARROW)),
+        (Index(list("ABC"), dtype=object), True),
         (MultiIndex.from_product([range(3), range(3)]), False),
-        (MultiIndex.from_product([range(3), ["foo", "bar"]]), True),
+        (
+            MultiIndex.from_product([range(3), ["foo", "bar"]]),
+            not (using_string_dtype() and HAS_PYARROW),
+        ),
     ],
 )
 def test_info_memory_usage_qualified(index, plus):