code: def stats_with_column_names(key, pdf):
      # order of column can be different to applyInPandas schema when column names are given
      return pd.DataFrame(
          [(pdf.v.mean(),) + key], columns=["mean", "id"]
      )
  
imports: import datetime
  import unittest
  from collections import OrderedDict
  from decimal import Decimal
  from typing import cast
  from pyspark.sql import Row
  from pyspark.sql.functions import array, explode, col, lit, udf, sum, pandas_udf, PandasUDFType, window
  from pyspark.sql.types import IntegerType, DoubleType, ArrayType, BinaryType, ByteType, LongType, DecimalType, ShortType, FloatType, StringType, BooleanType, StructType, StructField, NullType, MapType, YearMonthIntervalType
  from pyspark.errors import PythonException, PySparkTypeError
  from pyspark.testing.sqlutils import ReusedSQLTestCase, have_pandas, have_pyarrow, pandas_requirement_message, pyarrow_requirement_message
  from pyspark.testing.utils import QuietTest
label_desc: Use image node_id 12 for calling the GroupedApplyInPandasTestsMixin obj's underlying member method code with example usage: obj.stats_with_column_names(key, pdf) and returns: pd