# Calculating population standard deviation

This is a script I have written to calculate the population standard deviation. I feel that this can be simplified and also be made more pythonic.

from math import sqrt

def mean(lst):
"""calculates mean"""
sum = 0
for i in range(len(lst)):
sum += lst[i]
return (sum / len(lst))

def stddev(lst):
"""calculates standard deviation"""
sum = 0
mn = mean(lst)
for i in range(len(lst)):
sum += pow((lst[i]-mn),2)
return sqrt(sum/len(lst)-1)

numbers = [120,112,131,211,312,90]

print stddev(numbers)


The easiest way to make mean() more pythonic is to use the sum() built-in function.

def mean(lst):
return sum(lst) / len(lst)


Concerning your loops on lists, you don't need to use range(). This is enough:

for e in lst:
sum += e


• You don't need parentheses around the return value (check out PEP 8 when you have a doubt about this).
• Your docstrings are useless: it's obvious from the name that it calculates the mean. At least make them more informative ("returns the mean of lst").
• Why do you use "-1" in the return for stddev? Is that a bug?
• You are computing the standard deviation using the variance: call that "variance", not sum!
• You should type pow(e-mn,2), not pow((e-mn),2). Using parentheses inside a function call could make the reader think he's reading a tuple (eg. pow((e,mn),2) is valid syntax)
• You shouldn't use pow() anyway, ** is enough.

This would give:

def stddev(lst):
"""returns the standard deviation of lst"""
variance = 0
mn = mean(lst)
for e in lst:
variance += (e-mn)**2
variance /= len(lst)

return sqrt(variance)


It's still way too verbose! Since we're handling lists, why not using list comprehensions?

def stddev(lst):
"""returns the standard deviation of lst"""
mn = mean(lst)
variance = sum([(e-mn)**2 for e in lst]) / len(lst)
return sqrt(variance)


This is not perfect. You could add tests using doctest. Obviously, you should not code those functions yourself, except in a small project. Consider using Numpy for a bigger project.

• Thank you Cygal for your answer. I realize things like tests and validation need to be added, but I think you put me in the right direction. Feb 22, 2012 at 8:23
• @mad, I realize you're not able to comment due to your reputation, but if you see a problem in a post and want to fix it, you'll either have to be patient and wait until you have 50 reputation or go out, answer a question, and get five upvotes (or ask a good question and get 10). Please don't try to circumvent the system. Third-party edits should only edit the content of the post (as opposed to formatting, grammar, spelling, pasting in content from links etc.) with explicit approval from the poster.
– anon
Dec 30, 2015 at 20:09
• Looks like you forgot to divide the variance by N before taking the sqrt in the last/least verbose example. Sep 29, 2016 at 16:41
• @CodyA.Ray Your Rev 2 corrected the result, but it was not the right fix. Sep 29, 2016 at 19:19
• @200_success can you elaborate? Yeah, variance is the wrong variable name there. I could've just divided in the "return" line. But the equation seems correct for non-sampled std dev: libweb.surrey.ac.uk/library/skills/Number%20Skills%20Leicester/… Sep 29, 2016 at 22:09

You have some serious calculation errors…

Assuming that this is Python 2, you also have bugs in the use of division: if both operands of / are integers, then Python 2 performs integer division. Possible remedies are:

(Assuming that this is Python 3, you can just use statistics.stdev().

The formula for the sample standard deviation is

$$s = \sqrt{\frac{\sum_{i=1}^{n}\ (x_i - \bar{x})^2}{n - 1}}$$

In return sqrt(sum/len(lst)-1), you have an error with the precedence of operations. It should be

return sqrt(float(sum) / (len(lst) - 1))

• Source for formula? Mar 26, 2015 at 23:40
• @Agostino It's basically common knowledge in statistics. Mar 26, 2015 at 23:42