Post on 11-Jul-2015
Mirasol S. Madrid III-9 BS Psychology
Also called as z scores
Measures the difference
between the raw score and the
mean of the distribution using
standard deviation of the
distribution as a unit of
measurement
Reflects how many
standard deviations above
or below the mean a raw
score is
By itself, a raw score or X value provides very little information about how that particular score compares with other values in the distribution.
A score of X = 53, for example, may be a relatively low score, or an average score, or an extremely high score depending on the mean and standard deviation for the distribution from which the score was obtained.
50 60 70 80403020
0 1 2 3-1-2-3
x
z
If the raw score is transformed into a z-score, however, the value of the z-score tells exactly where the score is located relative to all the other scores in the distribution.
𝑧 =(𝑥 − 𝑥)
𝑠Where:
Z = standard score/z-score
X = Raw Score
𝒙 = Mean
S = Standard Deviation
𝑧 =(𝑥 − 𝜇)
𝜎Where:
Z = standard score/z-score
X = Raw Score
𝝁 = Mean
𝝈 = (sigma) Standard Deviation
Z-scores can be positive (above the mean), negative (below the mean), or zero (equal to the mean)
In a distribution of statistic test score,
having the mean of 75 and a standard deviation
of 10, find the z score, scoring 85
X = 85
𝑥 = 75
S = 10
1. Step 1
𝑧 =(85 − 75)
102. Step 2
𝑧 =(10)
10z = 1
A score of 85 is one (1)
standard deviation
above the mean
Find the Z score of 60
having a mean of 75
and a standard
deviation of 10
X = 60
𝑥 = 75
S = 10
1. Step 1
𝑧 =(55 − 75)
102. Step 2
𝑧 =(−20)
10z= -2
A score of 60 is two (2)
standard deviation
below the mean
X = 100
𝑥 = 100
S = 10
1. Step 1
𝑧 =(100 − 100)
102. Step 2
𝑧 =(0)
10z= 0
A score of 100 is falls
on the given mean.
1. X = 58, µ = 50, σ = 10
2. X = 74, µ = 65, σ = 6
3. X = 47, µ = 50, σ = 5
4. X = 87, µ = 100, σ = 8
5. X = 22, µ = 15, σ = 5
1. z = +.8
2. z = +1.5
3. z = -.6
4. z = -1.625
5. z = +1.4