prirodnogbk

2022-07-02

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.

$z=\frac{x-\mu}{\sigma}$

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.

Adolfo Rich

Beginner2022-07-03Added 9 answers

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.

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