# Is the definition of z-score correct?

I'm taking a course in Statistics, and I'm confused by the following wording which popped up on one of the lessons. Does the explanation sound correct? Are there any terms that are imprecise?

Q: We can best describe the location of the sample mean in a sampling distribution in terms of:

A: Standard error

Explanation: We'll describe the location of the sample mean by calculating how many standard errors it is away from the center of the sampling distribution. That will give us a z-score for our sample mean.

## 1 Answer

Looks fine to me. z-score equals "observed value of thing, minus expected value of thing, divided by standard deviation of thing". The only slight weakness in the description above is that it doesn't mention that the z-score is negative when the sample mean (i.e. the observed mean of the sample) is smaller than the centre of the sampling distribution (i.e. the expected value of the sample mean).