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Let's say a list of numbers $L$ has standard deviation $S$. Is there a formula for finding $S$ if I remove an element $l$ from $L$? Assume we know the mean of both $L$ and $L - l$.

Stephan Kolassa
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Mistakamikaze
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    The question of updating the sample variance as one (or more) new datapoints becomes available is one of [tag:online-algorithms]. So you can simply take an established algorithm and change it to yield the "old" variance based on the "new" variance, the data point to be removed and supplementary information like the "old" and "new" means. – Stephan Kolassa Mar 29 '21 at 09:16
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    One (amusing) solution method is to view this as a combination of a dataset of size $n$ and another one of size $-1,$ enabling you to apply (without change) [formulas for updating moments](https://stats.stackexchange.com/a/51927/919) when datasets are combined. – whuber Mar 29 '21 at 12:43

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