Newbie question on central limit theorem and standard error

Hi all:

First post here, hopefully in the right forum.

I'm trying to teach myself basic stats (using the book Statistics in a Nutshell) and I'm trying to get my head round something. The book gives a brief discussion of the Central Limit Theorem, and then says that it shows:


So (given large enough sample) the distribution of the sample mean should approximate a normal distribution with a mean equal to the population mean and a standard deviation equal to the population variance over the sample size.

So far so good, except, is the standard deviation of the sampling mean not the same as standard error? And is standard error not calculated as:


In fact, the book later shows this, and I'm struggling to follow, since the two are clearly quite different. Is this something to do with the fact that the second formula is using sample standard deviations? Or have I got something drastically wrong and the standard deviation of the distribution of the sample mean is not standard error?

Can anyone help?


Billy, in your first "So..." statement, replace "standard deviation" with "variance," or replace "variance over the sample size" with "standard deviation over the square root of the sample size." And yes, it may be referred to as "standard error of the mean."