May of the measures that are of interest
in psychology are distributed in the following
manner:
1) the majority of scores are near the mean
2) the more deviant a score is from the mean
the less frequently it appears
3) when large numbers of observations are made
the distribution has a smooth, symmetrical
shape.
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Normal Curve or Distribution
Standard Deviations
Note: this is a frequency Polygon
Ordinate = Frequency
Abscissa = Standard Deviations
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Normal Curve or Distribution
tails
Standard Deviations
Note: This curve is Asymptotic
Tails never touch the abscissa (there are no ends)
Represents idea that no extreme is ever impossible
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Standard Normal Curve or Distribution
Standard Deviations
Since there are no ends, we use the Mean
of the distribution as the reference point.
Mean = 0s
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Standard Deviation (s)
- average distance of the scores in the distribution
from the mean.
What does the word mean?
Deviant - different
- the larger s is for a distribution of data
the more spread out the data.
Standard - Measurement unit
- a set amount used to compare other
things to.
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Standard Deviation is a measurement unit we use
to assess how different one data score is from
the mean of the distribution of observations
Example: Height in men X = 5’9” s = 2
John is 5’11”
How many s is he from the mean?
Pat is 5’9
How many s is he from the mean?
Ron is 5’5”?
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Kate’s height is 2 s from the mean.
Bridget’s is - 3 s from the mean.
Who is Taller?
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If you know how many standard deviations you
are from the mean you can estimate your
percentile rank in the population.
1) Your z score is your number of s from the
mean
z = (Your score - Mean)/Standard Deviation
z 
Score  Mean
s
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Normal Curve or Distribution
Standard Deviations
We can determine the percentage of scores
that fall between the mean and any place on
the normal curve.
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Your Test Score = 84%
Class Mean = 74%
Standard Deviation = 5
z score = (Score - mean)/ standard deviation
Measure of how many standard deviations your score is away
from the mean.
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If the Standard Deviation was 10 what would the z score be?
For a normal distribution we can determine the percentage
of scores below (or above) any score.
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Z-scores allow us to compare our standings (percentile position) in
two classes. Since the mean and standard deviations of the two
classes are not the same, it is very possible that a person could have a
higher class standing in a class in which they had a lower test score.
In the following example, the mean for each exam is 50, but they
differ on their standard deviations.
Class A
Mean = 50
s = 10
Class B
Mean = 50
s=5
z =(60 – 50)/10 = +1.0
z = (60 – 50)/5 = +2.0
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84th percentile
97th percentile
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