blocks|key|1308055|text|下面这个简短的“手动计算”如何？|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1308056|def+weighted_avg_and_std(values,+weights):
++++"""
++++Return+the+weighted+average+and+standard+deviation.

++++values,+weights+--+Numpy+ndarrays+with+the+same+shape.
++++"""
++++average+=+numpy.average(values,+weights=weights)
++++#+Fast+and+numerically+precise:
++++variance+=+numpy.average((values-average)**2,+weights=weights)
++++return+(average,+math.sqrt(variance))|code-block|syntax|javascript|1308057|entityMap^0|0|0^^$0|@$1|2|3|4|5|6|7|I|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|J|8|@]|9|@]|A|$E|F]]|$1|G|3|-4|5|6|7|K|8|@]|9|@]|A|$]]]|H|$]]

How about the following short "manual calculation"?

<pre><code>def weighted_avg_and_std(values, weights):
 """
 Return the weighted average and standard deviation.

 values, weights -- Numpy ndarrays with the same shape.
 """
 average = numpy.average(values, weights=weights)
 # Fast and numerically precise:
 variance = numpy.average((values-average)**2, weights=weights)
 return (average, math.sqrt(variance))
</code></pre>

blocks|key|1308092|text|这里还有一个选择：|type|unstyled|depth|inlineStyleRanges|entityRanges|data|1308093|np.sqrt(np.cov(values,+aweights=weights))|code-block|syntax|javascript|1308094|entityMap^0|0|0^^$0|@$1|2|3|4|5|6|7|I|8|@]|9|@]|A|$]]|$1|B|3|C|5|D|7|J|8|@]|9|@]|A|$E|F]]|$1|G|3|-4|5|6|7|K|8|@]|9|@]|A|$]]]|H|$]]

Here's one more option:

<pre><code>np.sqrt(np.cov(values, aweights=weights))
</code></pre>

blocks|key|1308036|text|在numpy/scipy中似乎还没有这样的功能，但是有一个ticket提出了这个附加功能。在这里，你会发现Statistics.py实现了加权标准差。|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|1308037|entityMap|0|LINK|mutability|MUTABLE|url|https://github.com/scipy/scipy/issues/1131|1|http://projects.scipy.org/scipy/attachment/ticket/604/Statistics.py^0|T|6|0|1H|D|1|0^^$0|@$1|2|3|4|5|6|7|N|8|@]|9|@$A|O|B|P|1|Q]|$A|R|B|S|1|T]]|C|$]]|$1|D|3|-4|5|6|7|U|8|@]|9|@]|C|$]]]|E|$F|$5|G|H|I|C|$J|K]]|L|$5|G|H|I|C|$J|M]]]]

There doesn't appear to be such a function in numpy/scipy yet, but there is a <a href="https://github.com/scipy/scipy/issues/1131" rel="nofollow noreferrer">ticket</a> proposing this added functionality. Included there you will find <a href="http://projects.scipy.org/scipy/attachment/ticket/604/Statistics.py" rel="nofollow noreferrer">Statistics.py</a> which implements weighted standard deviations.

blocks|key|1092987|text|gaborous提出了一个很好的例子|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|1092988|import+pandas+as+pd
import+numpy+as+np
#+X+is+the+dataset,+as+a+Pandas'+DataFrame
mean+=+mean+=+np.ma.average(X,+axis=0,+weights=weights)+#+Computing+the+
weighted+sample+mean+(fast,+efficient+and+precise)

#+Convert+to+a+Pandas'+Series+(it's+just+aesthetic+and+more+
#+ergonomic;+no+difference+in+computed+values)
mean+=+pd.Series(mean,+index=list(X.keys()))+
xm+=+X-mean+#+xm+=+X+diff+to+mean
xm+=+xm.fillna(0)+#+fill+NaN+with+0+(because+anyway+a+variance+of+0+is+
just+void,+but+at+least+it+keeps+the+other+covariance's+values+computed+
correctly))
sigma2+=+1./(w.sum()-1)+*+xm.mul(w,+axis=0).T.dot(xm);+#+Compute+the+
unbiased+weighted+sample+covariance|code-block|syntax|javascript|1092989|Correct+equation+for+weighted+unbiased+sample+covariance,+URL+(version:+2016-06-28)|1092990|entityMap|0|LINK|mutability|MUTABLE|url|https://stats.stackexchange.com/users/25538/gaborous|1|https://stats.stackexchange.com/q/61298^0|0|8|0|0|0|0|2B|1|0^^$0|@$1|2|3|4|5|6|7|U|8|@]|9|@$A|V|B|W|1|X]]|C|$]]|$1|D|3|E|5|F|7|Y|8|@]|9|@]|C|$G|H]]|$1|I|3|J|5|6|7|Z|8|@]|9|@$A|10|B|11|1|12]]|C|$]]|$1|K|3|-4|5|6|7|13|8|@]|9|@]|C|$]]]|L|$M|$5|N|O|P|C|$Q|R]]|S|$5|N|O|P|C|$Q|T]]]]

There is a very good example proposed by <a href="https://stats.stackexchange.com/users/25538/gaborous">gaborous</a>:

<pre><code>import pandas as pd
import numpy as np
# X is the dataset, as a Pandas' DataFrame
mean = mean = np.ma.average(X, axis=0, weights=weights) # Computing the 
weighted sample mean (fast, efficient and precise)

# Convert to a Pandas' Series (it's just aesthetic and more 
# ergonomic; no difference in computed values)
mean = pd.Series(mean, index=list(X.keys())) 
xm = X-mean # xm = X diff to mean
xm = xm.fillna(0) # fill NaN with 0 (because anyway a variance of 0 is 
just void, but at least it keeps the other covariance's values computed 
correctly))
sigma2 = 1./(w.sum()-1) * xm.mul(w, axis=0).T.dot(xm); # Compute the 
unbiased weighted sample covariance
</code></pre>

<a href="https://stats.stackexchange.com/q/61298">Correct equation for weighted unbiased sample covariance, URL (version: 2016-06-28)</a>

blocks|key|1308120|text|对"frequency+weights“意义上的”样本“或”无偏“标准差的后续，因为”加权样本标准差python“谷歌搜索导致了这篇文章：|type|unstyled|depth|inlineStyleRanges|entityRanges|offset|length|data|1308121|def+frequency_sample_std_dev(X,+n):
++++"""
++++Sample+standard+deviation+for+X+and+n,
++++where+X[i]+is+the+quantity+each+person+in+group+i+has,
++++and+n[i]+is+the+number+of+people+in+group+i.
++++See+Equation+6.4+of:
++++Montgomery,+Douglas,+C.+and+George+C.+Runger.+Applied+Statistics+
+++++and+Probability+for+Engineers,+Enhanced+eText.+Available+from:+
++++++WileyPLUS,+(7th+Edition).+Wiley+Global+Education+US,+2018.
++++"""
++++n_groups+=+len(n)
++++n_people+=+sum(n)
++++lhs_numerator+=+sum([ni*Xi**2+for+Xi,+ni+in+zip(X,+n)])
++++rhs_numerator+=+sum([Xi*ni+for+Xi,+ni+in+zip(X,n)])**2/n_people
++++denominator+=+n_people-1
++++var+=+(lhs_numerator+-+rhs_numerator)+/+denominator
++++std+=+sqrt(var)
++++return+std|code-block|syntax|javascript|1308122|或者修改@Eric的答案如下：|1308123|def+weighted_sample_avg_std(values,+weights):
++++"""
++++Return+the+weighted+average+and+weighted+sample+standard+deviation.

++++values,+weights+--+Numpy+ndarrays+with+the+same+shape.
++++
++++Assumes+that+weights+contains+only+integers+(e.g.+how+many+samples+in+each+group).
++++
++++See+also+https://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Frequency_weights
++++"""
++++average+=+np.average(values,+weights=weights)
++++variance+=+np.average((values-average)**2,+weights=weights)
++++variance+=+variance*sum(weights)/(sum(weights)-1)
++++return+(average,+sqrt(variance))

print(weighted_sample_avg_std(X,+n))|1308124|entityMap|0|LINK|mutability|MUTABLE|url|https://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Frequency_weights^0|2|H|0|0|0|0|0^^$0|@$1|2|3|4|5|6|7|U|8|@]|9|@$A|V|B|W|1|X]]|C|$]]|$1|D|3|E|5|F|7|Y|8|@]|9|@]|C|$G|H]]|$1|I|3|J|5|6|7|Z|8|@]|9|@]|C|$]]|$1|K|3|L|5|F|7|10|8|@]|9|@]|C|$G|H]]|$1|M|3|-4|5|6|7|11|8|@]|9|@]|C|$]]]|N|$O|$5|P|Q|R|C|$S|T]]]]

A follow-up to &quot;sample&quot; or &quot;unbiased&quot; standard deviation in the &quot;<a href="https://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Frequency_weights" rel="nofollow noreferrer">frequency weights</a>&quot; sense since &quot;weighted sample standard deviation python&quot; Google search leads to this post:
<pre class="lang-py prettyprint-override"><code>def frequency_sample_std_dev(X, n):
 &quot;&quot;&quot;
 Sample standard deviation for X and n,
 where X[i] is the quantity each person in group i has,
 and n[i] is the number of people in group i.
 See Equation 6.4 of:
 Montgomery, Douglas, C. and George C. Runger. Applied Statistics 
 and Probability for Engineers, Enhanced eText. Available from: 
 WileyPLUS, (7th Edition). Wiley Global Education US, 2018.
 &quot;&quot;&quot;
 n_groups = len(n)
 n_people = sum(n)
 lhs_numerator = sum([ni*Xi**2 for Xi, ni in zip(X, n)])
 rhs_numerator = sum([Xi*ni for Xi, ni in zip(X,n)])**2/n_people
 denominator = n_people-1
 var = (lhs_numerator - rhs_numerator) / denominator
 std = sqrt(var)
 return std
</code></pre>
Or modifying the answer by @Eric as follows:
<pre class="lang-py prettyprint-override"><code>def weighted_sample_avg_std(values, weights):
 &quot;&quot;&quot;
 Return the weighted average and weighted sample standard deviation.

 values, weights -- Numpy ndarrays with the same shape.
 
 Assumes that weights contains only integers (e.g. how many samples in each group).
 
 See also https://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Frequency_weights
 &quot;&quot;&quot;
 average = np.average(values, weights=weights)
 variance = np.average((values-average)**2, weights=weights)
 variance = variance*sum(weights)/(sum(weights)-1)
 return (average, sqrt(variance))

print(weighted_sample_avg_std(X, n))
</code></pre>

<code>numpy.average()</code> has a weights option, but <code>numpy.std()</code> does not. Does anyone have suggestions for a workaround?

Weighted standard deviation in NumPy

翻译质量差，导致语言生硬或混乱。

没有提供实际的解决方法或示例。

解答不清晰，无法理解或解决问题。

页面排版不美观，阅读体验差。

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numpy.average()有一个权重选项，但numpy.std()没有。有没有人有解决办法的建议？

问NumPy中的加权标准差
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