list - Need to take average of long, strangely formatted set of data in Python -

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so have large set of data looks 

[('art', [100, 234, 830, 304]), ('math', [600, 1400, 300, 340]), ('history', [2010, 300,   400, 600])]

how turn set of data can average numbers inside of , sort? i'm using python 2.7

for:

input = [('art', [100, 234, 830, 304]),           ('math', [600, 1400, 300, 340]),           ('history', [2010, 300, 400, 600])]

this:

print sorted( ( (k,sum(v)/len(v)) k,v in input ), key=lambda t: t[1] )

prints:

[('art', 367), ('math', 660), ('history', 827)]

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