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/