I have been reading a Statistics book and they show the following formula for z-score:
$ z = \frac{x - \mu}{\sigma}$
And then they explain about the $\mu$ and the $\sigma$ in the formula like this:
These are the mean and standard deviation of data containing the value x.
But is that so ? I don't think the mean and standard deviation should contain the value x.
x comes from some distribution which has a fixed mean and standard deviation, determined before x was generated - you shouldn't be thinking of standard deviations and means of a finite set of numbers here.