2. What if.... You recently finished taking a test that you received a score of 90 It was out of 200 points The highest score was 110 The average score was 95 The lowest score was 90

3. Z-score A mathematical way to modify an individual raw score so that the result conveys the score’s relationship to the mean and standard deviation of the other scores

4. Z-score Ingredients: X Raw score Mean of scores S The standard deviation of scores

5. Z-score

6. What it does x - Tells you how far from the mean you are and if you are > or < the mean S Tells you the “size” of this difference

7. Example Sample 1: X = 8 = 6 S = 5

8. Example Sample 1: X = 8 = 6 S = 5 Z score =.4

9. Example Sample 1: X = 8 = 6 S = 1.25

10. Example Sample 1: X = 8 = 6 S = 1.25 Z-score = 1.6

11. = 6 S = 5

12. = 6 S = 5 = 6 S = 1.25

13. = 6 S = 5 = 6 S = 1.25

14. X X = 6 S = 5 X = 8 Z =.4 = 6 S = 1.25 X = 8 Z=1.6

20. Practice SAT and GRE Mean = 500 S = 100 Your scores:Verbal = 400 Analyt = 500 Quant = 700 How did you do on each section?

21. Practice SAT and GRE Mean = 500 S = 100 Your scores:Verbal = 400Z = -1 Analyt = 500 Z = 0 Quant = 700Z = 2 How did you do on each section?

22. Practice The history teacher Mr. Hand announced that the lowest test score for each student would be dropped. Jeff scored a 85 on his first test. The mean was 74 and the SD was 4. On the second exam, he made 150. The class mean was 140 and the SD was 15. On the third exam, the mean was 35 and the SD was 5. Jeff got 40. Which test should be dropped?

23. Practice Test #1 Z = (85 - 74) / 4 = 2.75 Test #2 Z = (150 - 140) / 15 =.67 Test #3 Z = (40 - 35) / 5 = 1.00

24. Practice

25. Did Ross do worse in the endurance challenge then in the throwing challenge? Did Monica do better in the throwing challenge than the endurance?

26. Practice = 34.6 = 7.4 S = 7.12 S = 2.15

27. Practice = 34.6 = 7.4 S = 7.12 S = 2.15

28. Practice = 34.6 = 7.4 S = 7.12 S = 2.15

29. Ross did worse in the throwing challenge than the endurance and Monica did better in the endurance than the throwing challenge. = 34.6 = 7.4 S = 7.12 S = 2.15

30. Z-Scores A distribution of scores has a standard deviation = 10. Find the z-score corresponding to each of the following values. A score that is 20 points above the mean A score 10 points below the mean A score 15 points above the mean A score 30 points below the mean

31. Z-Scores A distribution of scores has a standard deviation = 10. Find the z-score corresponding to each of the following values. A score that is 20 points above the mean = 2.00 A score 10 points below the mean = -1.00 A score 15 points above the mean = 1.50 A score 30 points below the mean = -3.00

32. Z-Scores A score that is 12 points above the mean corresponds to a Z-score of Z = 2.00. What is the standard deviation for this population?

33. Z-Scores A score that is 12 points above the mean corresponds to a Z-score of Z = 2.00. What is the standard deviation for this population? 12 / y = 2 y = 6

34. One-Step Beyond For a population of exam scores, a score of X = 58 corresponds to Z =.50 and a score of X = 46 corresponds to Z = -1.00. Find the mean and standard deviation for the population.

35. Z-Scores 1. Sketch out the distribution to help 2. Notice that the difference between the two raw scores (X = 58 and X = 46) is 12 raw units. 3. Notice the difference between the two raw scores is 1.5 SD.

36. Z-Scores 4. Thus, 1.5 (SD) = 12 5. SD = 8 6. Plug in the SD into either Z-score formula

37. Z-Scores 7. Z score = 46 - y / 8 = -1.00 Z score = 46 - 54 / 8 = -1.00 Mean = 54! SD = 8