Sorry, corrected second try because of copy&paste mistakes: VlG-Arne > Comments appreciated.
> Definition var_samp = Sum of squared differences /n-1 > Definition stddev_samp = sqrt(var_samp) > Example N=4 > 1.) Sum of squared differences > 1_4Sum(Xi-XM4)² > = > 2.) adding nothing > 1_4Sum(Xi-XM4)² > +0 > +0 > +0 > = > 3.) nothing changed > 1_4Sum(Xi-XM4)² > +(-1_3Sum(Xi-XM3)²+1_3Sum(Xi-XM3)²) > +(-1_2Sum(Xi-XM2)²+1_2Sum(Xi-XM2)²) > +(-1_1Sum(Xi-XM1)²+1_1Sum(Xi-XM1)²) > = > 4.) parts reordered > (1_4Sum(Xi-XM4)²-1_3Sum(Xi-XM3)²) > +(1_3Sum(Xi-XM3)²-1_2Sum(Xi-XM2)²) > +(1_2Sum(Xi-XM2)²-1_1Sum(Xi-XM1)²) > +1_1Sum(X1-XM1)² > = > 5.) > (X4-XM4)(X4-XM3) > + (X3-XM3)(X3-XM2) > + (X2-XM2)(X2-XM1) > + (X1-XM1)² > = > 6.) XM1=X1 => There it is - The iteration part of Welfords Algorithm > (in > reverse order) > (X4-XM4)(X4-XM3) > + (X3-XM3)(X3-XM2) > + (X2-XM2)(X2-X1) > + 0 > The missing piece is 4.) to 5.) > it's algebra, look at e.g.: > http://jonisalonen.com/2013/deriving-welfords-method-for-computing-variance/ -- Sent via pgsql-hackers mailing list (pgsql-hackers@postgresql.org) To make changes to your subscription: http://www.postgresql.org/mailpref/pgsql-hackers
