Calculating sum of squared deviations in R

Question

How can I calculate the sum of squared deviations(from the mean) of a vector?

I tried using the command

sum(x-mean(x))^2

but unfortunately what this returns is -1.998401e-15 which cannot be right. Is there a subtle operator, like a parenthesis, that I am missing here perhaps?

Thanks.

Answer 1

It may well be correct. -2.0 to the power of 10^15 means it is essentially zero. But as Justin just noted in the comment, you have

    (sum (x - mean(x) )^2

when you probably meant:

    sum( (x - mean(x) )^2 )

Answer 2

You can also use another way to calculate the sum of squared deviations:

x <- 1:10 #an example vector

# the 'classic' approach
sum( (x - mean(x) )^2 )
# [1] 82.5

# based on the variance
var(x) * (length(x) - 1)
#[1] 82.5

The latter works because var(x) = (x - mean(x))^2) / (length(x) - 1). This is the sample variance: