Review
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Review Data: {1, 4, 7, 8, 2, 12, 8} What is the median? A.4 B.5 C.6 D.7 E.8
description
Review. Data: {1, 4, 7, 8, 2, 12, 8} What is the median? 4 5 6 7 8. Review. What scale type is this variable? Number of lever presses in a 5-min session Nominal Ordinal Interval Ratio. Review. What scale type is this variable? Points along Folsom St. between Valmont and Iris - PowerPoint PPT Presentation
Transcript of Review
Review
Data: {1, 4, 7, 8, 2, 12, 8}
What is the median?
A.4
B.5
C.6
D.7
E.8
Review
What scale type is this variable?
Number of lever presses in a 5-min session
A.Nominal
B.Ordinal
C.Interval
D.Ratio
Review
What scale type is this variable?
Points along Folsom St. between Valmont and Iris
A.Nominal
B.Ordinal
C.Interval
D.Ratio
Variability
9/11
Variability
• Central tendency locates middle of distribution• How are scores distributed around that point?• Low variability vs. high variability• Ways to measure variability
– Range– Interquartile range– Sum of squares– Variance– Standard deviation
012345
6789
10
3 4 5 6 7 8 9
Maze Attempts
Fre
qu
ency
(ra
ts)
012345
6789
10
1 2 3 4 5 6 7 8 9 10 11
Maze Attempts
Fre
qu
ency
(ra
ts)
Why Variability is Important
• Inference– Reliability of estimators
• For its own sake– Consistency (manufacturing, sports, etc.)– Diversity (attitudes, strategies)
49 58 100 61 97 55 31 52 13 43
178154 136 103 94 181 91 109 46 28
34 175 37 139 106 19 184 88 112 64
76 172 157 22 16 85 142 130 151 67
121124160 40 145 127 100 82 133 169
166 163 118 148 79 25 115 73 187 70
Average = 87.25
49 58 100 61 97 55 31 52 13 43
178 154 136 103 94 181 91 109 46 28
34175 37 139 106 19 184 88 112 64
76 172 157 22 16 85 142130151 67
121124160 40 145127100 82 133 169
166 163 118148 79 25 115 73 187 70
Average = 121
49 58 100 61 97 55 31 52 13 43
178154 136 103 94 181 91 109 46 28
34175 37 139 106 19 184 88 112 64
76 172 157 22 16 85 142 130 151 67
121124160 40 145 127 100 82 133169
166 163 118 148 79 25 115 73 187 70
Average = 111.63
100105100 108 108 99 97 106 104 106
93 108 96 105104109 93 97 100 104
99 96 105 95 93 92 100 103 103 97
102 92 94 96 108 98 99 101 106 94
95 102 94 93 99 101 102 107 92 97
105 95 96 107 101 107 92 102103 98
Average = 99.13
100105100 108 108 99 97 106104106
93 108 96 105 104 109 93 97 100 104
99 96 105 95 93 92 100103103 97
102 92 94 96 108 98 99 101 106 94
95 102 94 93 99 101102 107 92 97
105 95 96 107 101 107 92 102 103 98
Average = 100.5
100105 100 108 108 99 97 106 104 106
93 108 96 105104 109 93 97 100104
99 96 105 95 93 92 100103103 97
102 92 94 96 108 98 99 101 106 94
95 102 94 93 99 101 102 107 92 97
105 95 96 107101107 92 102 103 98
Average = 99.5
= 100
M99.1
100.599.5
M87.3121
111.6
Range
• Distance from minimum to maximum
• Sample range depends on n
• More useful as population parameter– Theoretical property of measurement variable– E.g. memory test: min and max possible– Rough guidelines, e.g. height
)min(-)max( XXrange
0123456789
10
1 2 3 4 5 6 7 8 9 10 11
Maze Attempts
Fre
qu
en
cy
(ra
ts)
Measurement unit or precision
(11 – 1) + 1 = 11
X = [66.2, 78.6, 69.6, 65.3, 62.7]
78.6 – 62.7 + .1 = 16.0
0123456789
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62
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66
68
70
72
74
76
78
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82
84
Height (Inches)
Fre
qu
ency
(st
ud
ents
)
0123456789
10
50
52
54
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58
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62
64
66
68
70
72
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78
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82
84
Height (Inches)
Fre
qu
ency
(st
ud
ents
)
0123456789
10
50
52
54
56
58
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62
64
66
68
70
72
74
76
78
80
82
84
Height (Inches)
Fre
qu
ency
(st
ud
ents
)
05
101520253035404550
50
52
54
56
58
60
62
64
66
68
70
72
74
76
78
80
82
84
Height (Inches)
Fre
qu
ency
(st
ud
ents
)
78.65 – 62.65 = 16.0
Interquartile range• Quartiles
– Values of X based on dividing data into quarters– 1st quartile: greater than 1/4 of data– 3rd quartile: greater than 3/4 of data– 2nd quartile = median
• Interquartile range– Difference between 1st and 3rd quartiles– Like range, but for middle half of distribution– Not sensitive to n more stable
X = [1,1,2,2,2,3,3,4,4,4,4,5,5,5,5,6,6,6,6,6,7,7,7,8]
3rd quartile = 61st quartile = 3
6 – 3 = 3
729 = 272
441 = 212
49 = 72
Sum of Squares• Based on deviation of each datum from the mean: (X – )• Square each deviation and add them up
11588 94 108 122 133 145
2721
7
71830
2 = 49 2 = 324 2 = 900
Variance
• Most sophisticated statistic for variability• Sum of squares divided by N
– Mean Square: average squared deviation
729 = 272
441 = 212
49 = 72
11588 94 108 122 133 145
2721
7
71830
2 = 49 2 = 324 2 = 900
• Typical difference between X and • Again, based on (X – )2
• Variance is average squared deviation,so sqrt(variance) is standard deviation
N
X
2
Standard deviation
N
X 2 2X 2X
X = [5, 3, 7, 6, 4, 6, 8, 7, 4, 2, 3, 5] = 5
X – = [0, -2, 2, 1, -1, 1, 3, 2, -1, -3, -2, 0]
(X – )2 = [0, 4, 4, 1, 1, 1, 9, 4, 1, 9, 4, 0]
Square
Average
Square-root
Average
Why squared difference?
• Could use absolute distances, |X - µ|– Would be more intuitive: average distance from the mean
• Squares have special mathematical properties– Can be broken into different parts
Sum of Squares:Differences among scores
Central Tendency:Common to all scores
Review
Ask people how many hats they own.
Data: {6, 4, 7, 8, 2, 12, 8}
What is the range?
A.2
B.7
C.10
D.11
E.12
Review
Find the sum of squares of {6, 4, 7, 8, 2, 9}.
Hint: M = 6
A.34
B.250
C.12
D.214
E.234
Review
A population has a sum of squares of 6400 and a variance of 16. How big is the population (N)?
A.5
B.20
C.400
D.1600
E.Not enough information
