As I understand, _decimal_to_ratio() should always produce an
integer ratio.  But it does not for positive exponents:

>>> import statistics
>>> statistics.mean([Decimal("100"), Decimal("200")])
Decimal('150')
>>> statistics.mean([Decimal("1e2"), Decimal("2e2")])
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "/usr/local/lib/python3.4/statistics.py", line 308, in mean
    return _sum(data)/n
  File "/usr/local/lib/python3.4/statistics.py", line 166, in _sum
    total += Fraction(n, d)
  File "/usr/local/lib/python3.4/fractions.py", line 163, in __new__
    raise TypeError("both arguments should be "
TypeError: both arguments should be Rational instances
>>> 
>>> statistics._decimal_to_ratio(Decimal("1e2"))     
(1, 0.01)
>>> 1e2.as_integer_ratio()
(100, 1)

See also issue 20561, which is a duplicate of this.

Fix and tests for this in the attached patch. Could somebody please commit it for me, my ssh key apparently hasn't been registered yet.

New changeset 0f9309f8c755 by Nick Coghlan in branch 'default':
Close #20536: correctly handle Decimal exponents in statistics
http://hg.python.org/cpython/rev/0f9309f8c755

Steven,
I think

if exp >= 0:
    return int(x), 1

would have been a better patch, but yours is certainly working, just slower I guess.