Computing means, variances and sums

p.s.  If my computations are correct, 0.2 = 0*/2 + 0/4 + 1/8 + 1/16 +
0/32 + 0/64 + 1/128 + 1/256 + 0/512 + 0/1024 + 1/2048 + 1/4096 + ... =
0.3333333333333h.  Perhaps someone can extend this to an FAQ to help
explain finite precision arithmetic and rounding issues.

This is drifting a bit off topic, but the other day I discovered this
rather nice illustration of the perils of finite precision arithmetic
while creating a contrast matrix:

n <- 13
a <- matrix(-1/n, ncol=n, nrow=n) + diag(n)
rowSums(a)

[1]  2.775558e-16  2.775558e-16  5.551115e-17  5.551115e-17  5.551115e-17
 [6]  5.551115e-17  0.000000e+00 -5.551115e-17  0.000000e+00  5.551115e-17
[11]  1.110223e-16  1.665335e-16  2.220446e-16

Not only do most of the rows not sum to 0, they do not even sum to the
same number!  It is hard to remember the familiar rules of arithmetic
do not always apply.

Hadley