Ultimately what I want is the mode of a column, for all the columns in the DataFrame. For other summary statistics, I see a couple of options: use DataFrame aggregation, or map the columns of the DataFrame to an RDD of vectors (something I'm also having trouble doing) and use colStats from MLlib. But I don't see mode as an option there.
A problem with mode is pretty much the same as with median. While it is easy to compute, computation is rather expensive. It can be done either using sort followed by local and global aggregations or using just-another-wordcount and filter:
import numpy as np
np.random.seed(1)
df = sc.parallelize([
(int(x), ) for x in np.random.randint(50, size=10000)
]).toDF(["x"])
cnts = df.groupBy("x").count()
mode = cnts.join(
cnts.agg(max("count").alias("max_")), col("count") == col("max_")
).limit(1).select("x")
mode.first()[0]
## 0
Either way it may require a full shuffle for each column.