1. STATISTICS EXERCISE u EDUCATIONAL RESEARCH

2. Organizing Data: An Array 19 23 71 56 17 32 95 23 17 95 71 56 32 23 19 17

3. Array: Quiz Scores u 14.75 12 11.5 13.5 14.75 14.75 13 12.5 13.5 u 14.75 u 13.50 u 13.00 u 12.50 u 12.00 u 11.50

4. 2.Frequency (f) - u Cumulative frequency (cf) -

5. u Frequency Example 1: Weights u XTallies fcf u 95 1 19 u 71 1 18 u 56 1 17 u 32 1 16 u 23 1 1 25 u 19 1 13 u 17 1 1 22

6. u Frequency Example 2: Quiz scores u XTalliesfcf u 14.751 1 139 u 13.501 126 u 13.00114 u 12.50113 u 12.00112 u 11.5111

7. u SUMMATION u WeightsQuiz scores u 9514.75 u 7114.75 u 5614.75 u 3213.50 u 2313.50 u 2313.00 u 1912.50 u 1712.00 u 1711.50 u 353120.25

8. u Putting it All Together Weights u Xfcffx u 951995 u 711871 u 561756 u 321632 u 232546 u 191319 u 172234 u n = 9 = 353

9. u Putting it All Together Quiz scores u Xfcffx u 14.753944.25 u 13.502627.00 u 13.001413.00 u 12.501312.50 u 12.001212.00 u 11.501111.50 u n = 9 = 120.25

10. u Mean Weights u = 353 / 9 u = 39.22 u Mean Quiz Scores u = 120.25 / 9 u = 13.36

11. u Mode (Mo) Weights u 95 u 71 u 56 u 32 u 23 u 19 u 17 u Mo = 17 & 23 -- bimodal

12. u Mode Quiz Scores u 14.75 u 13.50 u 13.00 u 12.50 u 12.00 u 11.50 u Mo = 14.75

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

14. u Situations where calculating the median will NOT be so easy. Consider: u 7 7 7 8 8 8 9 9 10 10 u Mdn = L +[ ( n / 2 - cfb) / fw) } i u 7.5 + { ( 10 / 2 - 3 ) / 3 } 1 u = 7.5 + (5 - 3) / 3} 1 u = 7.5 + (2 / 3) 1 u = 8.17

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

16. u Deviation Scores u x (little x) = X (test score) - Mean u Example 1: Weights

17. u Score X X - Mean x2 u 95 55.783111.41 u 71 31.781009.97 u 56 16.78 281.57 u 32 -7.22 52.13 u 23 -16.22 263.09 u 19 -20.22 408.85 u 17 -22.22 493.73 u n = 9 x2=6377.57 u Sum = 353 Mean = 39.22

18. u Example 2: Quiz Scores u XX - Mean x2 u 14.75 1.391.93 u 13.50 0.140.02 u 13.00 -0.360.13 u 12.50 -0.860.74 u 12.00 -1.361.85 u 11.50 -1.863.46 u n = 9 = 0x2 = 12.01 u Mean = 13.36

19. u Example 1: Weights u sigma 2 = 6377.63 / 9 u = 708.63 u Example 2: Quiz Scores u sigma 2 = 12.01 / 9 u = 1.33

20. u Example 1: Weights u sigma = square root { 63377.63 / 9} u = square root {708. 63} u = 26.62 u Example 2: Quiz Scores u sigma = square root {1.33} u = 1.15

21. u Standard Scores u z-scores u Mean = 0 Standard Deviation = 1 u Equation: z = (X - Mean) / sigma u Mean of raw score distribution u sigma = SD of raw score distribution

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

23. u English z-score = ( 84 - 110) / 26 u = - 26 / 26 u z = - 1.00 u Algebra z-score = ( 40 - 47) / 5 u = -7 / 5 u z = -1.4

24. u English T-score = 50 + 10 (-1.00) u T = 50 + -10 u T = 40.00 u Algebra T-score = 50 + 10 (-1.4) u T = 50 + -14.00 u T = 36.00

25. u FINISHED--DONE-- COMPLETED u AT LONG, LONG LAST