Finding smallest float in file then printing that and line above it

Store the items in a list of lists,[word,num] pairs and then apply min on that list of list. Use key parameter of min to specify the which item must be used for comparison of item.:

with open('abc') as f:
    lis = [[line.strip(),next(f).strip()] for line in f]
    minn = min(lis, key = lambda x: float(x[1]))
    print "\n".join(minn)
...     
Over
0.5678

Here lis looks like this:

[['3.6-band', '6238'], ['Over', '0.5678'], ['Over', '0.6874'], ['Over', '0.7680'], ['Over', '0.7834']]