Shorten Python/Maya Window UI code
(1) You define random_scatter as a class but then call it like a function, which works but is confusing. With your programme as it currently stands, there is no reason for it to be a class, so better simply to define random_scatter as a function (use def random_scatter(): at the top). 

(2) You can remove repetition and make the code more readable using functions and loops, e.g. write a function

def insert_seperators(number):
    for _ in range(number):
        cmds.separator(height=20, style='in')


then you can replace 

    cmds.separator( height=20, style='in')
    cmds.separator( height=20, style='in')
    cmds.separator( height=20, style='in')


with

    insert_separators(3)


(3) If you have other functions doing similar things with cmds then try to see what they have in common and put that in a single function, which accepts parameters according to what changes.