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Understanding z scores
Standard scores
 Standard scores assume a normal distribution
 They provide a method of expressing any score in
a distribution in terms of its distance from the
mean in standard deviation units
2
Z-score
 A raw score by itself is rather meaningless.
 What gives the score meaning is its deviation
from the mean
 A Z score expresses this value in standard
deviation units
3
Z-score
z=
X =
Raw score
X =
Mean
s =
x=
X-X
s
or
x
s
Standard deviation
(X - X )
4
Z score formula
z=
X-X
s
or
x
s
X = 76
X = 82
s =4
5
Z score computation
z=
X-X
s
or
x
X = 76
s
X = 82
s =4
76 - 82 - 6
z=
=
= -1.50
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