STATISTICS EXERCISE

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STATISTICS EXERCISE

• EDUCATIONAL RESEARCH

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Organizing Data An Array

• 19 23 71 56 17 32 95
  23 17
• 95
• 71
• 56
• 32
• 23
• 23
• 19
• 17
• 17

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Array Quiz Scores

• 14.75 12 11.5 13.5 14.75 14.75 13
  12.5 13.5
• 14.75
• 14.75
• 14.75
• 13.50
• 13.50
• 13.00
• 12.50
• 12.00
• 11.50

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• 2. Frequency (f) -
• Cumulative frequency (cf) -

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• Frequency Example 1 Weights
• X Tallies f cf
• 95 1 1 9
• 71 1 1 8
• 56 1 1 7
• 32 1 1 6
• 23 1 1 2 5
• 19 1 1 3
• 17 1 1 2 2

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• Frequency Example 2 Quiz scores
• X Tallies f cf
• 14.75 1 1 1 3 9
• 13.50 1 1 2 6
• 13.00 1 1 4
• 12.50 1 1 3
• 12.00 1 1 2
• 11.5 1 1 1

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• SUMMATION
• Weights Quiz scores
• 95 14.75
• 71 14.75
• 56 14.75
• 32 13.50
• 23 13.50
• 23 13.00
• 19 12.50
• 17 12.00
• 17 11.50
• 353 120.25

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• Putting it All Together Weights
• X f cf fx
• 95 1 9 95
• 71 1 8 71
• 56 1 7 56
• 32 1 6 32
• 23 2 5 46
• 19 1 3 19
• 17 2 2 34
• n 9 353

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• Putting it All Together Quiz scores
• X f cf fx
• 14.75 3 9 44.25
• 13.50 2 6 27.00
• 13.00 1 4 13.00
• 12.50 1 3 12.50
• 12.00 1 2 12.00
• 11.50 1 1 11.50
• n 9 120.25

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• Mean Weights
• 353 / 9
• 39.22
• Mean Quiz Scores
• 120.25 / 9
• 13.36

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• Mode (Mo) Weights
• 95
• 71
• 56
• 32
• 23
• 23
• 19
• 17
• 17
• Mo 17 23 -- bimodal

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• Mode Quiz Scores
• 14.75
• 14.75
• 14.75
• 13.50
• 13.50
• 13.00
• 12.50
• 12.00
• 11.50
• Mo 14.75

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• 3. Median (Mdn)
• Group A Group B
• X X
• 7 50
• 6 6
• 5 5
• 4 -- Mdn 4 -- Mdn
• 3 3
• 2 2
• 1 0

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• Situations where calculating the median will NOT
  be so easy. Consider
• 7 7 7 8 8 8 9 9
  10 10
• Mdn L ( n / 2 - cfb) / fw) i
• 7.5 ( 10 / 2 - 3 ) / 3 1
• 7.5 (5 - 3) / 3 1
• 7.5 (2 / 3) 1
• 8.17

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• E. Measures of Variability
• 1. Range
• R Xh - Xl
• Example 1 Weights
• R 95 - 17 78
• Example 2 Quiz Scores
• R 14.75 - 11.5 3.25

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• Deviation Scores
• x (little x) X (test score) - Mean
• 
  
  Example 1 Weights

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• Score X X - Mean x2
• 95 55.78 3111.41
• 71 31.78 1009.97
• 56 16.78 281.57
• 32 -7.22 52.13
• 23 -16.22 263.09
• 23 -16.22 263.09
• 19 -20.22 408.85
• 17 -22.22 493.73
• 17 -22.22 493.73
• n 9 x26377.57
• Sum 353 Mean 39.22

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• Example 2 Quiz Scores
• X X - Mean x2
• 14.75 1.39 1.93
• 14.75 1.39 1.93
• 14.75 1.39 1.93
• 13.50 0.14 0.02
• 13.50 0.14 0.02
• 13.00 -0.36 0.13
• 12.50 -0.86 0.74
• 12.00 -1.36 1.85
• 11.50 -1.86 3.46
• n 9 0 x2 12.01
• Mean 13.36

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• Example 1 Weights
• sigma 2 6377.63 / 9
• 708.63
• Example 2 Quiz Scores
• sigma 2 12.01 / 9
• 1.33

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• Example 1 Weights
• sigma square root 63377.63 / 9
• square root 708. 63
• 26.62
• Example 2 Quiz Scores
• sigma square root 1.33
• 1.15

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• Standard Scores
• z-scores
• Mean 0 Standard Deviation 1
• Equation z (X - Mean) / sigma
• Mean of raw score distribution
• sigma SD of raw score distribution

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• b. T-scores
• Mean 50 SD 10
• Equation T 50 10 (z)
• Example Let's suppose that a teacher wants to
  compare the results of an English and of an
  Algebra test
• Test Score Mean Highest SD
• English 84 110 180 26
• Algebra 40 47 60 5

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• English z-score ( 84 - 110) / 26
• - 26 / 26
• z - 1.00
• Algebra z-score ( 40 - 47) / 5
• -7 / 5
• z -1.4

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• English T-score 50 10 (-1.00)
• T 50 -10
• T 40.00
• Algebra T-score 50 10 (-1.4)
• T 50 -14.00
• T 36.00

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• FINISHED--DONE--COMPLETED
• AT LONG, LONG LAST

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