diff --git a/modin/experimental/core/storage_formats/pandas/small_query_compiler.py b/modin/experimental/core/storage_formats/pandas/small_query_compiler.py
index d6767478926..75f2130cea4 100644
--- a/modin/experimental/core/storage_formats/pandas/small_query_compiler.py
+++ b/modin/experimental/core/storage_formats/pandas/small_query_compiler.py
@@ -18,6 +18,8 @@
 queries for small data and empty ``PandasDataFrame``.
 """
 
+from typing import Optional
+
 import numpy as np
 import pandas
 from pandas.core.dtypes.common import is_list_like, is_scalar
@@ -587,7 +589,11 @@ def caller(query_compiler, *args, **kwargs):
         args = try_cast_to_pandas(args, squeeze=squeeze_args)
         kwargs = try_cast_to_pandas(kwargs, squeeze=squeeze_kwargs)
         result = func(df, *args, **kwargs)
+        inplace_method = kwargs.get("inplace", False)
+
         if in_place:
+            inplace_method = in_place
+        if inplace_method:
             result = df
         if not (return_modin or isinstance(result, (pandas.Series, pandas.DataFrame))):
             return result
@@ -692,7 +698,6 @@ def setitem_bool(self, row_loc, col_loc, item):
     cumprod = _register_default_pandas(pandas.DataFrame.cumprod)
     cumsum = _register_default_pandas(pandas.DataFrame.cumsum)
     delitem = _register_default_pandas(_delitem)
-    describe = _register_default_pandas(pandas.DataFrame.describe)
     df_update = _register_default_pandas(
         pandas.DataFrame.update, in_place=True, df_copy=True
     )
@@ -855,7 +860,7 @@ def setitem_bool(self, row_loc, col_loc, item):
     )
     isna = _register_default_pandas(pandas.DataFrame.isna)
     join = _register_default_pandas(pandas.DataFrame.join)
-    kurt = _register_default_pandas(pandas.DataFrame.kurt)
+    kurt = _register_default_pandas(pandas.DataFrame.kurt, return_modin=False)
     last_valid_index = _register_default_pandas(
         pandas.DataFrame.last_valid_index, return_modin=False
     )
@@ -866,7 +871,7 @@ def setitem_bool(self, row_loc, col_loc, item):
     max = _register_default_pandas(pandas.DataFrame.max)
     map = _register_default_pandas(pandas.DataFrame.map)
     mean = _register_default_pandas(pandas.DataFrame.mean, return_modin=False)
-    median = _register_default_pandas(pandas.DataFrame.median)
+    median = _register_default_pandas(pandas.DataFrame.median, return_modin=False)
     melt = _register_default_pandas(pandas.DataFrame.melt)
     memory_usage = _register_default_pandas(pandas.DataFrame.memory_usage)
     merge = _register_default_pandas(pandas.DataFrame.merge)
@@ -964,7 +969,7 @@ def setitem_bool(self, row_loc, col_loc, item):
     series_view = _register_default_pandas(pandas.Series.view, is_series=True)
     set_index_from_columns = _register_default_pandas(pandas.DataFrame.set_index)
     setitem = _register_default_pandas(_setitem)
-    skew = _register_default_pandas(pandas.DataFrame.skew)
+    skew = _register_default_pandas(pandas.DataFrame.skew, return_modin=False)
     sort_index = _register_default_pandas(_sort_index)
     sort_columns_by_row_values = _register_default_pandas(
         lambda df, columns, **kwargs: df.sort_values(by=columns, axis=1, **kwargs)
@@ -1057,6 +1062,13 @@ def clip(self, lower, upper, **kwargs):
             self, lower, upper, **kwargs
         )
 
+    def describe(self, percentiles: np.ndarray):
+        return _register_default_pandas(pandas.DataFrame.describe)(
+            self,
+            percentiles=percentiles,
+            include="all",
+        )
+
     def dot(self, other, squeeze_self=None, squeeze_other=None):
         other = try_cast_to_pandas(other)
         if squeeze_other:
@@ -1223,3 +1235,24 @@ def getitem_column_array(self, key, numeric=False, ignore_order=False):
 
     def is_series_like(self):
         return len(self._modin_frame.columns) == 1 or len(self._modin_frame.index) == 1
+
+    def support_materialization_in_worker_process(self) -> bool:
+        """
+        Whether it's possible to call function `to_pandas` during the pickling process, at the moment of recreating the object.
+
+        Returns
+        -------
+        bool
+        """
+        True
+
+    def get_pandas_backend(self) -> Optional[str]:
+        """
+        Get backend stored in `_modin_frame`.
+
+        Returns
+        -------
+        str | None
+            Backend name.
+        """
+        return None
diff --git a/modin/pandas/series.py b/modin/pandas/series.py
index 749cf0f6a50..4df41168b5a 100644
--- a/modin/pandas/series.py
+++ b/modin/pandas/series.py
@@ -31,10 +31,7 @@
 from pandas.io.formats.info import SeriesInfo
 from pandas.util._validators import validate_bool_kwarg
 
-from modin.config import PersistentPickle, UsePlainPandasQueryCompiler
-from modin.experimental.core.storage_formats.pandas.small_query_compiler import (
-    PlainPandasQueryCompiler,
-)
+from modin.config import PersistentPickle
 from modin.logging import disable_logging
 from modin.pandas.io import from_pandas, to_pandas
 from modin.utils import (
@@ -147,32 +144,18 @@ def __init__(
                 name = MODIN_UNNAMED_SERIES_LABEL
                 if isinstance(data, pandas.Series) and data.name is not None:
                     name = data.name
-            if UsePlainPandasQueryCompiler.get():
-                query_compiler = PlainPandasQueryCompiler(
-                    pandas.DataFrame(
-                        pandas.Series(
-                            data=data,
-                            index=index,
-                            dtype=dtype,
-                            name=name,
-                            copy=copy,
-                            fastpath=fastpath,
-                        )
+            query_compiler = from_pandas(
+                pandas.DataFrame(
+                    pandas.Series(
+                        data=data,
+                        index=index,
+                        dtype=dtype,
+                        name=name,
+                        copy=copy,
+                        fastpath=fastpath,
                     )
                 )
-            else:
-                query_compiler = from_pandas(
-                    pandas.DataFrame(
-                        pandas.Series(
-                            data=data,
-                            index=index,
-                            dtype=dtype,
-                            name=name,
-                            copy=copy,
-                            fastpath=fastpath,
-                        )
-                    )
-                )._query_compiler
+            )._query_compiler
         self._query_compiler = query_compiler.columnarize()
         if name is not None:
             self.name = name