Thread: Standard deviation

How come standard deviation is sometimes calculated
http://www.cs.utexas.edu/users/scott...tandardDev.gif
and sometimes
with the same formula but n instead of n-1 in the denominator?[/tex]

Originally Posted by thyristor

How come standard deviation is sometimes calculated
http://www.cs.utexas.edu/users/scott...tandardDev.gif
and sometimes
with the same formula but n instead of n-1 in the denominator?[/tex]

The population standard deviation is calculated with "n". It is the standard deviation of a random variable defined on a domain of n points.

The calculation that uses "n-1" is the sample standard deviation. It is the best unbiased estimate of the standard deviation of a population, possibly infinite, based on a sample. The sample standard deviation is itself a random variable.

This is usually explained in terms of variance, variance being the more fundamental quantity, the square root of which is the standard deviation. See the discussion of population variance and sample variance in this Wiki article.

http://en.wikipedia.org/wiki/Variance

As Dr Rocket said, if you try to estimate the std deviation using the 1\n version, after you have first estimated the mean, you will on average underestimate the thing you are trying to calculate.

[edit - fixed typo]

A simple explanation:

If you know the mean exactly, use 1/n. If you use the sample average to estimate the mean, use 1/(n-1) to take into account the uncertainty in the mean.

Ok, thanks for your replies.