Pandas: Group by date and the median of another variable

I would do this :

df['date'] = df['date'].apply(lambda x : x.date())
df = df.groupby('date').agg({'sentiment':np.median}).reset_index()

You first replace the datetime column with the date. Then you perform the groupby+agg operation.

You fortunately have the tools you need listed in your question.

In [61]: df.groupby(df.date.dt.date)[['sentiment']].median()
Out[61]:
            sentiment
2015-05-26        0.9
2015-05-27        0.5
2015-05-28        0.7