How to calculate daily averages from noon to noon with pandas?

The base argument.

A day is 24 hours, so a base of 12 would start the grouping from Noon - Noon. Resample gives you all days in between, so you could .dropna(how='all') if you don't need the complete basis. (I assume you have a DatetimeIndex, if not you can use the on argument of resample to specify your datetime column.)

df.resample('24H', base=12).mean()
#df.groupby(pd.Grouper(level=0, base=12, freq='24H')).mean() # Equivalent 

                         1      2          3
0                                           
2014-03-31 12:00:00  54.20  41.30  52.233333
2014-04-01 12:00:00  50.75  39.35  34.950000
2014-04-02 12:00:00    NaN    NaN        NaN
2014-04-03 12:00:00    NaN    NaN        NaN
2014-04-04 12:00:00    NaN    NaN        NaN
...                    ...    ...        ...
2016-11-26 12:00:00    NaN    NaN        NaN
2016-11-27 12:00:00    NaN    NaN        NaN
2016-11-28 12:00:00    NaN    NaN        NaN
2016-11-29 12:00:00    NaN    NaN        NaN
2016-11-30 12:00:00  17.80  15.45  40.450000

You could subtract your time and groupby:

df.groupby((df.index - pd.to_timedelta('12:00:00')).normalize()).mean()