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# Practice PowerPoint PPT Presentation

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

Practice

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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

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?

 =

( )

( )

= 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