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# alexalemi/welford.py

Created March 21, 2012 19:29
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Python Welford Algorithm
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 import math class Welford(object): """ Implements Welford's algorithm for computing a running mean and standard deviation as described at: http://www.johndcook.com/standard_deviation.html can take single values or iterables Properties: mean - returns the mean std - returns the std meanfull- returns the mean and std of the mean Usage: >>> foo = Welford() >>> foo(range(100)) >>> foo >>> foo([1]*1000) >>> foo >>> foo.mean 5.409090909090906 >>> foo.std 16.44374171455467 >>> foo.meanfull (5.409090909090906, 0.4957974674244838) """ def __init__(self,lst=None): self.k = 0 self.M = 0 self.S = 0 self.__call__(lst) def update(self,x): if x is None: return self.k += 1 newM = self.M + (x - self.M)*1./self.k newS = self.S + (x - self.M)*(x - newM) self.M, self.S = newM, newS def consume(self,lst): lst = iter(lst) for x in lst: self.update(x) def __call__(self,x): if hasattr(x,"__iter__"): self.consume(x) else: self.update(x) @property def mean(self): return self.M @property def meanfull(self): return self.mean, self.std/math.sqrt(self.k) @property def std(self): if self.k==1: return 0 return math.sqrt(self.S/(self.k-1)) def __repr__(self): return "".format(self.mean, self.std)

### ghost commented Jul 16, 2012

Works great and saved me a bit of time, thanks :)

### hamx0r commented Apr 12, 2016

Great gist! moving `self.k += 1` until after `newM` and `newS` are calculated adds robustness for cases where someone tries to use this with strings or other non-numeric types....the function will then throw an error before incrementing `k`, thus preserving the accuracy of the data within their Welford instance.

### ugiacoman commented Jun 12, 2016

Beautiful! You'd be surprised at how many incorrect versions of Welford are online, thanks!

### gerardsimons commented Feb 27, 2020 • edited

Nice code! One minor thing: not sure if returning an std of 0 is appropriate in the case of k=1 though as this is confusing when k != 0 but std = 0?

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