Z-score

Z-score is a way for us to explain how many standard deviations we are from the center(0)

So a z-score of 2 will mean we are 2 standard deviations from the mean

Z-Score formula

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

Standardization

We are able to turn any Normal Distributions into a Standard Normal Distribution For example, this distribution: $\mu$ = 50 $\sigma$ = 25.81988897

Perform z-scores of all the data points:

x	z-score of x
10	-1.54919338
20	-1.161895004
30	-0.774596669
40	-0.487298334
50	0
60	0.387289334
70	0.774596669
80	1.161895004
90	1.549193338

Z-Score Table

The z-score table is a table to tell us the percentile rank of the distribution a z-score means. You need to combine a column and row and you get the area (<X) to the left(the percentile rank). so 3.49 will be the row 3.4 and the column 0.09