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Revision of {{oldid|Algorithms for calculating variance|270157362|12 February 2009}} further "corrected" titles by eliminating roman numerals. Today's revision of {{oldid|Algorithms for calculating variance|707525590}} replaced roman numerical references from the text according to the above map. [[User:Ale2006|ale]] ([[User talk:Ale2006|talk]]) 10:32, 29 February 2016 (UTC)
Issues with the section called "Welford's online algorithm".
1. I don't see the point of these equations:
{\displaystyle s_{n}^{2}={\frac {n-2}{n-1}}\,s_{n-1}^{2}+{\frac {(x_{n}-{\bar {x}}_{n-1})^{2}}{n}}=s_{n-1}^{2}+{\frac {(x_{n}-{\bar {x}}_{n-1})^{2}}{n}}-{\frac {s_{n-1}^{2}}{n-1}},\quad n>1}
{\displaystyle \sigma _{n}^{2}={\frac {(n-1)\,\sigma _{n-1}^{2}+(x_{n}-{\bar {x}}_{n-1})(x_{n}-{\bar {x}}_{n})}{n}}=\sigma _{n-1}^{2}+{\frac {(x_{n}-{\bar {x}}_{n-1})(x_{n}-{\bar {x}}_{n})-\sigma _{n-1}^{2}}{n}}.} {\displaystyle \sigma _{n}^{2}={\frac {(n-1)\,\sigma _{n-1}^{2}+(x_{n}-{\bar {x}}_{n-1})(x_{n}-{\bar {x}}_{n})}{n}}=\sigma _{n-1}^{2}+{\frac {(x_{n}-{\bar {x}}_{n-1})(x_{n}-{\bar {x}}_{n})-\sigma _{n-1}^{2}}{n}}.}
They are just scaled versions of the equation that follows. I recommend removal.
2. The comment "These formulas suffer from numerical instability, as they repeatedly subtract a small number from a big number which scales with n." is confusing. It looks to me like some of the formulas repeatedly add a small number to a large number. In this respect they are no worse than the equation that follows.
3. The advantage of the {\displaystyle M_{2,n}} recurrence is that it is simpler and more computationally efficient because there are fewer multiplications and no divisions.
4. The last two equations should be
{\displaystyle {\begin{aligned}s_{n}^{2}&={\frac {M_{2,n}}{n-1}}\\[4pt]\sigma _{n}^{2}&={\frac {M_{2,n}}{n}}\end{aligned}}}
[[User:ProfRB|ProfRB]] ([[User talk:ProfRB|talk]]) 18:51, 22 March 2019 (UTC)
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