Standard Scores
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Transcript of Standard Scores
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Mirasol S. Madrid III-9 BS Psychology
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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
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Reflects how many
standard deviations above
or below the mean a raw
score is
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By itself, a raw score or X value provides very little information about how that particular score compares with other values in the distribution.
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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.
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50 60 70 80403020
0 1 2 3-1-2-3
x
z
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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.
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𝑧 =(𝑥 − 𝑥)
𝑠Where:
Z = standard score/z-score
X = Raw Score
𝒙 = Mean
S = Standard Deviation
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𝑧 =(𝑥 − 𝜇)
𝜎Where:
Z = standard score/z-score
X = Raw Score
𝝁 = Mean
𝝈 = (sigma) Standard Deviation
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Z-scores can be positive (above the mean), negative (below the mean), or zero (equal to the mean)
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In a distribution of statistic test score,
having the mean of 75 and a standard deviation
of 10, find the z score, scoring 85
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X = 85
𝑥 = 75
S = 10
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1. Step 1
𝑧 =(85 − 75)
102. Step 2
𝑧 =(10)
10z = 1
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A score of 85 is one (1)
standard deviation
above the mean
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Find the Z score of 60
having a mean of 75
and a standard
deviation of 10
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X = 60
𝑥 = 75
S = 10
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1. Step 1
𝑧 =(55 − 75)
102. Step 2
𝑧 =(−20)
10z= -2
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A score of 60 is two (2)
standard deviation
below the mean
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X = 100
𝑥 = 100
S = 10
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1. Step 1
𝑧 =(100 − 100)
102. Step 2
𝑧 =(0)
10z= 0
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A score of 100 is falls
on the given mean.
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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
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1. z = +.8
2. z = +1.5
3. z = -.6
4. z = -1.625
5. z = +1.4