Standard Deviation in R Seems to be Returning the Wrong Answer – Am I Doing Something Wrong?

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Try this 

R> sd(c(2,4,4,4,5,5,7,9)) * sqrt(7/8)
[1] 2
R>

and see the rest of the Wikipedia article for the discussion about estimation of standard deviations. Using the formula employed ‘by hand’ leads to a biased estimate, hence the correction of sqrt((N-1)/N). Here is a key quote:

The term standard deviation of the
sample is used for the uncorrected
estimator (using N) while the term
sample standard deviation is used for
the corrected estimator (using N − 1).
The denominator N − 1 is the number of
degrees of freedom in the vector of
residuals, .

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