Z-score = (x-mean) / SD
= the number of standard deviations a datum is from the mean of the data set.
Convert a datum x to its distance in SDs from the mean of the data set.

Data set mapped/transformed/normalized to z-scores:
each datum x: its number of SDs from the mean:     x → z
  z = (x-mean) / SD

 x    z
---  ---
 x̄ →  0
x̄+s → 1
x̄+1.5s → 1.5
x̄+2s → 2
x̄+3s → 3
x̄-s → -1
x̄-2s → -2

Within ±2 is "usual". [2,2]

≤-2 (-∞,-2] or ≥2 [2,∞) is "statistically significant",
i.e. maybe important.



mean=100  SD=10    Do this group in your head.
             x=100  z=________
x=90  z=________               x=110  z=________
x=80  z=________               x=120  z=________
x=70  z=________               x=130  z=________

x=95  z=________               x=105  z=________
x=85  z=________               x=115  z=________
x=75  z=________               x=125  z=________



mean=127  SD=12    Do this group by hand/head.
             x=127  z=________
x=115  z=________               x=139  z=________
x=103  z=________               x=151  z=________
x=91   z=________               x=163  z=________

Or use the SW: 	
x→Z-score→CDF ***

x=121 z=________               x=133  z=________
x=109 z=________               x=145  z=________
x=97  z=________               x=157  z=________