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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 = 78Range = 55

  • Mary = 78, 79, 77, 78, 78

    • Mean = 78Range = 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 range1

Interquartile Range

50%


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


Practice

= 16


Practice

= 16


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?


How about

How about?


How about1

How about?


Formula

Formula


Formula1

Formula

 =


Practice

( )


Practice

( )

= 6


Practice

( )

= 6


Practice

( )

= 6


Practice

( )

 = 38

= 6


Practice8

Practice

  • What is the standard deviation of:

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

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


Practice

( )

 = 1000

= 60


Practice

( )

 = 170

= 60


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