How can I use a Series to scalar pandas UDF to perform a mean aggregation on a Spark DataFrame column using the groupBy operation?
You can use a Series to scalar pandas UDF to perform a mean aggregation on a Spark DataFrame column using the groupBy operation as follows:

1. Import the required libraries:
```python
import pandas as pd
from pyspark.sql.functions import pandas_udf
```
2. Create a Spark DataFrame:
```python
df = spark.createDataFrame([(1, 1.0), (1, 2.0), (2, 3.0), (2, 5.0), (2, 10.0)], ("id", "v"))
```
3. Declare the function and create the UDF:
```python
@pandas_udf("double")
def mean_udf(v: pd.Series) -> float:
    return v.mean()
```
4. Use the UDF with the groupBy operation:
```python
df.groupby("id").agg(mean_udf(df['v'])).show()
```
This will output the following DataFrame:
```css
+---+-----------+
| id|mean_udf(v)|
+---+-----------+
| 1|        1.5|
| 2|        6.0|
+---+-----------+
```
The `mean_udf` function takes a pandas Series as input and returns the mean of the values in the Series. The `pandas_udf` decorator is used to specify the input and output types of the UDF. The `groupBy` operation is used to group the DataFrame by the "id" column, and the `agg` function is used to apply the UDF to the "v" column. The resulting DataFrame contains the mean values of the "v" column for each group.