Statistics with Python
A variable name input is confusing. After all, input is a Python built-in.
standard_deviation calls mean too many times (add a debug printout to mean to see). Better do

def standard_deviation(input):
    input_mean = mean(input)
    return math.sqrt(mean([(x - input_mean) ** 2 for x in input]))

Median can be calculated in \$ O(\log n)\$. Sorting a list in \$O(n \log n)\$ just for a median is an overkill.