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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

  • Order of operations

  • For the set of data:

  • 4, -2, 0, -1, -4

  • Calculate:

  • X (X)2 X2


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

  • Joe = 78, 60, 92, 80, 80

  • Bob = 47, 100, 98, 45, 100

  • Mary = 78, 79, 77, 78, 78


Variability

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


Range

  • The highest score minus the lowest score

  • Joe = 78, 60, 92, 80, 80

  • Range = 92 - 60 = 32


Range

  • The highest score minus the lowest score

  • Bob = 47, 100, 98, 45, 100

  • Range = 100 - 45 = 55


Range

  • The highest score minus the lowest score

  • Mary = 78, 79, 77, 78, 78

  • Range = 79 - 77 = 2


The Test Scores of 3 Students

  • Joe = 78, 60, 92, 80, 80

    • Mean = 78 Range = 32

  • Bob = 47, 100, 98, 45, 100

    • Mean = 78Range = 55

  • Mary = 78, 79, 77, 78, 78

    • Mean = 78Range = 2


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


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


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

  • 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 Range

50%


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 Range

IQR = 75th percentile - 25th percentile


Interquartile Range

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


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 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 Range

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

IQR = 75th percentile - 25th percentile

56 = 62 - 6


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


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


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


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


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


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

  • Most popular statistic used to describe variability

    S = a sample’s standard deviation

     = a population’s standard deviation


Deviation Score Formula

  • Deviation scores


= 16


= 16


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 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

  • 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?


How about?


How about?


Formula


Formula

 =


( )


( )

= 6


( )

= 6


( )

= 6


( )

 = 38

= 6


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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