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Practice. Order of operations For the set of data: 4, -2, 0, -1, -4 Calculate: X (X) 2 X 2. Practice. Order of operations For the set of data: 4, -2, 0, -1, -4 Calculate: X = -3 (X) 2 =9 X 2 =37. The Test Scores of 3 Students. Joe = 78, 60, 92, 80, 80

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Practice
Practice

  • Order of operations

  • For the set of data:

  • 4, -2, 0, -1, -4

  • Calculate:

  • X (X)2 X2


Practice1
Practice

  • Order of operations

  • For the set of data:

  • 4, -2, 0, -1, -4

  • Calculate:

  • X = -3 (X)2=9 X2=37


The test scores of 3 students
The Test Scores of 3 Students

  • Joe = 78, 60, 92, 80, 80

  • Bob = 47, 100, 98, 45, 100

  • Mary = 78, 79, 77, 78, 78


Variability
Variability

  • Provides a quantitative measure of the degree to which scores in a distribution are spread out or clustered together


Range
Range

  • The highest score minus the lowest score

  • Joe = 78, 60, 92, 80, 80

  • Range = 92 - 60 = 32


Range1
Range

  • The highest score minus the lowest score

  • Bob = 47, 100, 98, 45, 100

  • Range = 100 - 45 = 55


Range2
Range

  • The highest score minus the lowest score

  • Mary = 78, 79, 77, 78, 78

  • Range = 79 - 77 = 2


The test scores of 3 students1
The Test Scores of 3 Students

  • Joe = 78, 60, 92, 80, 80

    • Mean = 78 Range = 32

  • Bob = 47, 100, 98, 45, 100

    • Mean = 78 Range = 55

  • Mary = 78, 79, 77, 78, 78

    • Mean = 78 Range = 2


Range3
Range

  • In general - the larger the range score, the more variance

  • Pro: Easy to calculate

  • Con: The range only depends on two extreme scores; can be misleading


Range4
Range

20, 62, 54, 32, 28, 44, 72, 69, 50

1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,5, 5, 5, 5, 5, 99


Range5
Range

20, 62, 54, 32, 28, 44, 72, 69, 50

Range = 52

1, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5,5, 5, 5, 5, 5, 99

Range = 98!!


Interquartile range
Interquartile Range

  • The range of scores that make up the middle 50 percent of the distribution

  • Need to find the 25th percentile score and the 75th percentile score



Interquartile range2
Interquartile Range

.25 (N) = The location of the 25th percentile score counting from the bottom

.25 (N) = The location of the 75th percentile score counting from the top

N = the number of cases

*If the answer is not even simply average

*Similar to how you found the median!!


Interquartile range3
Interquartile Range

IQR = 75th percentile - 25th percentile


Interquartile range4
Interquartile Range

2, 5, 6, 10, 14, 16, 29, 40, 56, 62, 82, 99


Interquartile range5
Interquartile Range

2, 5, 6, 10, 14, 16, 29, 40, 56, 62, 82, 99

.25 (12) = 3

Counting 3 from the bottom the 25th percentile score = 6


Interquartile range6
Interquartile Range

2, 5, 6, 10, 14, 16, 29, 40, 56, 62, 82, 99

.25 (12) = 3

Counting 3 from the top the 75th percentile score = 62


Interquartile range7
Interquartile Range

2, 5, 6, 10, 14, 16, 29, 40, 56, 62, 82, 99

IQR = 75th percentile - 25th percentile

56 = 62 - 6


Practice2
Practice

  • Find the range for:

  • 8, 4, 10, 15, 25, 56, 76, 64, 43, 4, 56, 22

  • 8.5, 68.2, 78.3, 59.5, 78.6, 75.2, 12.9, 3.2

  • 102.58, 51.25, 58.00, 96.34, 54.43


Practice3
Practice

  • Find the range for:

  • 8, 4, 10, 15, 25, 56, 76, 64, 43, 4, 56, 22

    • Range =76 - 4 = 72

  • 8.5, 68.2, 78.3, 59.5, 78.6, 75.2, 12.9, 3.2

    • Range = 78.6 - 3.2 = 75.4

  • 102.58, 51.25, 58.00, 96.34, 54.43

    • Range = 102.58 - 51.25 = 51.33


Practice4
Practice

  • Find the interquartile range for:

  • 8, 4, 10, 15, 25, 56, 76, 64, 43, 4, 56, 22

  • 8.5, 68.2, 78.3, 59.5, 78.6, 75.2, 12.9, 3.2

  • 102.58, 51.25, 58.00, 96.34, 54.43


Practice5
Practice

  • Find the interquartile range for:

  • 8, 4, 10, 15, 25, 56, 76, 64, 43, 4, 56, 22

  • 4, 4, 8, 10, 15, 22, 25, 43, 56, 56, 64, 76

  • (12) .25 = 3

  • 56 - 8 = 48


Practice6
Practice

  • Find the interquartile range for:

  • 8.5, 68.2, 78.3, 59.5, 78.6, 75.2, 12.9, 3.2

  • 3.2, 8.5, 12.9, 59.5, 68.2, 75.2, 78.3, 78.6

  • (8).25 = 2

  • 78.3 - 8.5 = 69.8


Practice7
Practice

  • Find the interquartile range for:

  • 102.58, 51.25, 58.00, 96.34, 54.43

  • 51.25, 54.43, 58.00, 96.34, 102.58

  • (5).25 = 1.25

  • (51.25+54.43)/2 = 52.84

  • (96.34+102.58)/2 = 99.46

  • 99.46-52.84 = 46.62


Standard deviation
Standard Deviation

  • Most popular statistic used to describe variability

    S = a sample’s standard deviation

     = a population’s standard deviation


Deviation score formula
Deviation Score Formula

  • Deviation scores




Sample 1 vs sample 2
Sample 1 vs. Sample 2

  • Sample 1:

    Raw scores: 15, 12, 17, 20

  • Sample 2:

    Raw scores: 26, 6, 1, 31


Sample 1 vs sample 21
Sample 1 vs. Sample 2

  • Sample 1:

    Raw scores: 15, 12, 17, 20

    Deviation scores: -1, -4, 1, 4

  • Sample 2:

    Raw scores: 26, 6, 1, 31

    Deviation scores: 10, -10, -15, 15


Deviation scores
Deviation Scores

  • As variability increases the absolute value of the deviation scores also goes up!

  • How can we use this information to create a measure of variability?





Formula1
Formula

 =



( )

= 6


( )

= 6


( )

= 6


( )

 = 38

= 6


Practice8
Practice

  • What is the standard deviation of:

    Class 1: 80, 40, 60, 70, 50

    Class 2: 60, 51, 69, 62, 58


( )

 = 1000

= 60


( )

 = 170

= 60


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