How to calculate 1st and 3rd quartiles?

By using pandas:

df.time_diff.quantile([0.25,0.5,0.75])


Out[793]: 
0.25    0.483333
0.50    0.500000
0.75    0.516667
Name: time_diff, dtype: float64

You can use np.percentile to calculate quartiles (including the median):

>>> np.percentile(df.time_diff, 25)  # Q1
0.48333300000000001

>>> np.percentile(df.time_diff, 50)  # median
0.5

>>> np.percentile(df.time_diff, 75)  # Q3
0.51666699999999999

Or all at once:

>>> np.percentile(df.time_diff, [25, 50, 75])
array([ 0.483333,  0.5     ,  0.516667])