Standard Deviation One-liner

[Ethan Furman]

Steven D'Aprano wrote:
> On Fri, 03 Jun 2011 13:09:43 -0700, Raymond Hettinger wrote:
> 
>> On Jun 3, 10:55 am, Billy Mays <no... at nohow.com> wrote:
>>> I'm trying to shorten a one-liner I have for calculating the standard
>>> deviation of a list of numbers.  I have something so far, but I was
>>> wondering if it could be made any shorter (without imports).
>>>
>>> Here's my function:
>>>
>>> a=lambda d:(sum((x-1.*sum(d)/len(d))**2 for x in
>>> d)/(1.*(len(d)-1)))**.5
>>>
>>> The functions is invoked as follows:
>>>
>>>  >>> a([1,2,3,4])
>>> 1.2909944487358056
>> Besides trying to do it one line, it is also interesting to write an
>> one-pass version with incremental results:
>>
>>   http://mathcentral.uregina.ca/QQ/database/QQ.09.06/h/murtaza2.html
> 
> I'm not convinced that's a good approach, although I haven't tried it. In 
> general, the so-called "computational formula" for variance is optimized 
> for pencil and paper calculations of small amounts of data, but is 
> numerically unstable.
> 
> See 
> 
> http://www.johndcook.com/blog/2008/09/26/comparing-three-methods-of-
> computing-standard-deviation/
> 
> http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance
> 
> 
> 
> I'll also take this opportunity to plug my experimental stats package, 
> which includes coroutine-based running statistics, including standard 
> deviation:
> 
>--> s = stats.co.stdev()
>--> s.send(3)
> nan

Look!  A NaN in the wild!  :)

~Ethan~