I'm very new to pandas so I hope this will have an easy answer (and I also appreciate all pointers to even the setup of the dataframe)
So let's say I have the following DataFrame:
D = pd.DataFrame({ i:{ "name":str(i),
                       "vector": np.arange(i,i+10),
                       "sq":i**2,
                       "gp":i%3 } for i in range(10) }).T
    gp  name sq  vector
0    0   0   0   [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
1    1   1   1   [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
2    2   2   4   [2, 3, 4, 5, 6, 7, 8, 9, 10, 11]
3    0   3   9   [3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
4    1   4   16  [4, 5, 6, 7, 8, 9, 10, 11, 12, 13]
5    2   5   25  [5, 6, 7, 8, 9, 10, 11, 12, 13, 14]
6    0   6   36  [6, 7, 8, 9, 10, 11, 12, 13, 14, 15]
7    1   7   49  [7, 8, 9, 10, 11, 12, 13, 14, 15, 16]
8    2   8   64  [8, 9, 10, 11, 12, 13, 14, 15, 16, 17]
9    0   9   81  [9, 10, 11, 12, 13, 14, 15, 16, 17, 18]
Now I would like to group by "gp" and get the mean of the "vector"
I've tried
D.groupby('gp').mean()
and even
D.groupby('gp').agg( np.mean )
but I get an error that there were no "numeric types" to be aggregated. So do np.arrays not work in pandas?
For me it works:
D.groupby('gp').apply(lambda x: x.vector.mean().mean())
I'm taking the mean twice, since you want the mean group value for the mean of the vector (don't you?).
Out[98]: 
gp
0     9.0
1     8.5
2     9.5
dtype: float64
If you want the mean vector, just take the mean once.
arrays in cell is not a good idea, you can convert the vector col to multi cols:
D = pd.DataFrame({ i:{ "name":str(i),
                       "vector": np.arange(i,i+10),
                       "sq":i**2,
                       "gp":i%3 } for i in range(10) }).T
df = pd.concat([D[["gp", "name", "sq"]], pd.DataFrame(D.vector.tolist(), index=D.index)], axis=1, keys=["attrs", "vector"])
print df.groupby([("attrs", "gp")]).mean()
here is the output:
                  vector                                                  
                  0    1    2    3    4     5     6     7     8     9
(attrs, gp)                                                          
0               4.5  5.5  6.5  7.5  8.5   9.5  10.5  11.5  12.5  13.5
1               4.0  5.0  6.0  7.0  8.0   9.0  10.0  11.0  12.0  13.0
2               5.0  6.0  7.0  8.0  9.0  10.0  11.0  12.0  13.0  14.0
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