Pandas - Reshape Dataframe

Question

I have the following dataframe:

  Time  AreaIn  AreaOut   Output
0   1    Area E  Area G    200
1   16   Area E  Area G    200
2   31   Area E  Area G    200
3   46   Area E  Area G    300
4   61   Area E  Area G    459
5   ...  ...     ...       ...
93  1396 Area E  Area G    600
94  1411 Area E  Area G    400   
95  1426 Area E  Area G    500   
96  1441 Area E  Area G    500    
97  1    Area H  Area F    600
98  16   Area H  Area F    600
99  31   Area H  Area F    600
100 46   Area H  Area F    600
101 61   Area H  Area F    116
102 ...  ...     ...       ...
189 1381 Area H  Area F    111
190 1396 Area H  Area F    600   
191 1411 Area H  Area F    600   
192 1426 Area H  Area F    400
193 1441 Area H  Area F    400

And I want to reshape it. The column 'Time' ranges from 1 to 1441 with 15 interval, but I want it to range from 1 to 1441 with 60 interval. While the 'Output' should be the average of every 4 rows (sum of every 4 rows divided by 4).

In this case the dataframe contains only two time series so the result should look like this:

   Time   AreaIn  AreaOut   Output
0   1     Area E  Area G    450
1   61    Area E  Area G    500
2   121   Area E  Area G    600
3   181   Area E  Area G    892
4   241   Area E  Area G    459
5   ...    ...     ...       ...
21  1261  Area E  Area G    810
22  1321  Area E  Area G    598   
23  1381  Area E  Area G    650   
24  1441  Area E  Area G    250    
25  1     Area H  Area F    600
26  61    Area H  Area F    987
27  121   Area H  Area F    0
28  181    Area H  Area F   211
29  241    Area H  Area F   116
30  ...    ...     ...      ...
44  1201   Area H  Area F   111
45  1261   Area H  Area F   332   
46  1321   Area H  Area F   551   
47  1381   Area H  Area F   726
49  1441   Area H  Area F   250 

However, I want to implement a generic solution that could work with more than two timeseries.

while using: df = df.groupby(pd.cut(df["Time"], np.arange(1, 1442, 60))).mean() I am getting the following result:

                 Time   Output
Time                         
(1, 61]           38.5   2351
(61, 121]         98.5   2752
(121, 181]        158.5  4323
(181, 241]        218.5  2523
(241, 301]        278.5  3456
(301, 361]        338.5  1653
(361, 421]        398.5  4361
(421, 481]        458.5  6543
(481, 541]        518.5  3245
(541, 601]        578.5  2434
(601, 661]        638.5  1387
(661, 721]        698.5  4456
(721, 781]        758.5  2534
(781, 841]        818.5  3424
(841, 901]        878.5  2376
(901, 961]        938.5  2656
(961, 1021]       998.5  3456
(1021, 1081]     1058.5  1212
(1081, 1141]     1118.5  3355
(1141, 1201]     1178.5  2466
(1201, 1261]     1238.5  3462
(1261, 1321]     1298.5  2344
(1321, 1381]     1358.5  2453
(1381, 1441]     1418.5  3256

Which groups the outputs of the two different time series and mixes up Area E - Area G with Area H - Area F. So I would like to keep those two time series separately.