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4320CentralTendencyS15NoAudioorTransitions.pptx4320 Descriptive Statistics
Central Tendency
1
2
Normal Distribution
99.9
INSERT new Figure from 4th edition here
Chapter 3
3
68%
95%
99%
4
Symbols
f = Frequency
N = Number of measures
Σ= Summation
X = Score / measurement
X= Mean
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Measures of Central Tendency
“Average”
Describe the middle characteristics of a set of scores.
Allow a score to be compared with the group of scores.
Three measures of central tendency.
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Measures of Central Tendency
Mode: The most frequent score of the distribution
Median: The point below which 50% of scores fall (most appropriate central tendency to use)
Mean: The arithmetic average of the scores in a distribution; The most commonly used measure of central tendency
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Mode
Case 1
X f
5 2
4 3
3 2
2 5
1 7
Mode =1
5,4,3,2,1,1,1,2,2,3,4,5,4,2,1,2,1,1,1
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Mode
Case 1
X f
5 2
4 3
3 2
2 5
1 7
Case 2
X f
8 7
7 3
6 2
5 5
1 7
Mode =1
Mode = 8 , 1
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Median
Point at which half of the scores are below and half are above.
Not a score.
Represents the 50th percentile
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Median
X
55
39
26
24
20
19
18
X
88
87
86
85
84
83
Median
Median = 85.5
X
150
120
86
85
50
40
Median = 85.5
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Mean X = Σ X / N
X
88
87
86
85
84
1
X
88
87
86
85
84
80
Σ =431 N = 6
X=431
6
X=71.83
X=510
6
X=85
Σ =510 N = 6
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Summation Notation
S =
N =
Mean =
Median =
Mode =
20, 20, 21, 21, 22, 19, 20, 19, 22, 18, 18, 20, 21, 18, 19, 18, 21, 26, 30
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Summation Notation
Highest to Lowest
30,26,22,22,21,21,21,21,20,20,20,20,19,19,19,18,18,18,18
19 samples
9 median (8 above, 8 below)
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Summation Notation
S = 393
N = 19
Mean = 20.68
Median = 20
Mode = 18, 20, 21
20, 20, 21, 21, 22, 19, 20, 19, 22, 18, 18, 20, 21, 18, 19, 18, 21, 26, 30
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