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Gibney
PSY230
Chapter 4 Variability
1
Chapter 4
Variability
Variability
• Measure of
the degree to which the
scores in a distribution are spread out or
clustered togethe
clustered together
• Helps describe the distribution
• Measure of how well an individual score
represents the distribution
Symmetrical distributions with different variability
Three measures of variability
• Range
• Standard deviation
Vi
• Variance
The Range
• The distance covered by the scores in a
distribution
•Completely determined by two extreme
scores
• Highest – lowest score = range
• Considered a crude, unreliable measure of
variability
Standard Deviation
• Uses the mean as a reference
• Measures variability by looking at how far
hi
f
t
h
each score
is from the mean
• Average distance from the mean
• Concept is simple formulas look scary
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PSY230
Chapter 4 Variability
2
Deviation is the distance from the
mean
Each score in a distribution has a corresponding
deviation score
Deviation score =
X 
μ
(score  mu)
Examples
• In a distribution where
μ
= 30, and X = 35 then
the deviation would be X
μ
or 3530 or 5
• In the same distribution where
μ
= 30 and X=25
the deviation would be X
μ
or 2530 or 5
• Note that the deviation score has 2 parts a sign
(+/) and a size
• In this case the first score (35) is 5 units above
the mean and the second score (25) is 5 units
below the mean
Logic
• If you want to find the AVERAGE distance
of each score from the mean it is only
logical to calculate the mean of the
deviation scores
• Easy to do
• Except. . .
Average Deviation Calculation
X
X
μ
8
3
1. Find the mean
∑
X/n
2. Subtract the mean
from each score
(deviation)
1
0
X
μ
3. Find the average
deviation
∑
(X
μ
)/n
Variance
• Cannot just calculate average distance from the
mean
• By definition it always has to add up to zero
• It is balanced
• Solution is to square each deviation score to get
rid of negative signs
• This results in a score called the variance
• Mean squared deviation is called the variance
Standard Deviation
• Variance is ok but not exactly what we had
in mind as a measure
• In order to correct for squaring the numbers
the last stem in computing the standard
deviation is to take the square root of the
variance
Variance
Deviation
Standard
=
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This note was uploaded on 01/05/2011 for the course PSYC 230 taught by Professor Delaney during the Spring '08 term at University of Arizona Tucson.
 Spring '08
 Delaney
 Psychology

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