Z-Score of Z_Scores... Legitimate Analysis?

#1
(newbie question...)

i have a list of z_Scores for a particular dataset. is it a legitimate to find the z-score of a z-score against a set of z-scores..

so trying to find out how far this particular z-score is compared to a set of z-scores.

Anything wrong with this type of analysis? is this a legitimate way to analyze Z-Score?
 
#2
(newbie question...)

i have a list of z_Scores for a particular dataset. is it a legitimate to find the z-score of a z-score against a set of z-scores..

so trying to find out how far this particular z-score is compared to a set of z-scores.

Anything wrong with this type of analysis? is this a legitimate way to analyze Z-Score?
I would encourage you to try it and see what happens.

But, have you learned what the mean and the standard deviation ALWAYS are for a standardized (or z-score) distribution?

If so, think about those numbers, and about what would happen when you plug them into the z-score formula, and you'll see that what you're talking about doing is rather pointless (other than as a learning exercise).
 
#3
if they're all z-scores, i.e. each z~N(0,1), then standardizing them again does nothing, we're just subtracting 0 and dividing by 1