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Practice

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- Order of operations
- For the set of data:
- 4, -2, 0, -1, -4
- Calculate:
- X (X)2 X2

- Order of operations
- For the set of data:
- 4, -2, 0, -1, -4
- Calculate:
- X= -3 (X)2=9 X2=37

- Joe = 78, 60, 92, 80, 80
- Bob = 47, 100, 98, 45, 100
- Mary = 78, 79, 77, 78, 78

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

- The highest score minus the lowest score
- Joe = 78, 60, 92, 80, 80
- Range = 92 - 60 = 32

- The highest score minus the lowest score
- Bob = 47, 100, 98, 45, 100
- Range = 100 - 45 = 55

- The highest score minus the lowest score
- Mary = 78, 79, 77, 78, 78
- Range = 79 - 77 = 2

- 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

- 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

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

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!!

- 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%

.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!!

IQR = 75th percentile - 25th percentile

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

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

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

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

IQR = 75th percentile - 25th percentile

56 = 62 - 6

- 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

- 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

- 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

- 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

- 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

- 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

- Most popular statistic used to describe variability
S = a sample’s standard deviation

= a population’s standard deviation

- Deviation scores

= 16

= 16

- Sample 1:
Raw scores:15, 12, 17, 20

- Sample 2:
Raw scores:26, 6, 1, 31

- 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

- 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

- What is the standard deviation of:
Class 1: 80, 40, 60, 70, 50

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

( )

= 1000

= 60

( )

= 170

= 60