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Practice

Practice. 2.34 2.35 2.46. Review. Ways to “see” data Simple frequency distribution Group frequency distribution Histogram Stem-and-Leaf Display Describing distributions Box-Plot Measures of central tendency Mean Median Mode. Review. Measures of variability Range IQR

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Practice

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  1. Practice 2.34 2.35 2.46

  2. Review • Ways to “see” data • Simple frequency distribution • Group frequency distribution • Histogram • Stem-and-Leaf Display • Describing distributions • Box-Plot • Measures of central tendency • Mean • Median • Mode

  3. Review • Measures of variability • Range • IQR • Standard deviation

  4. Compute a standard deviation with the Raw-Score Method • Previously learned the deviation formula • Good to see “what's going on” • Raw score formula • Easier to calculate than the deviation formula • Not as intuitive as the deviation formula • They are algebraically the same!!

  5. Raw-Score Formula -1

  6. Step 1: Create a table

  7. Step 2: Square each value

  8. Step 3: Sum

  9. Step 4: Plug in values -1 N = 5 X = 44  X2 = 640

  10. Step 4: Plug in values 5 5 - 1 N = 5 X = 44  X2 = 640

  11. Step 4: Plug in values 44 5 5 - 1 N = 5 X = 44  X2 = 640

  12. Step 4: Plug in values 44 640 5 5 - 1 N = 5 X = 44  X2 = 640

  13. Step 5: Solve! 1936 44 640 5 5 - 1

  14. Step 5: Solve! 1936 44 640 387.2 5 4

  15. Step 5: Solve! 1936 44 63.2 640 387.2 5 5 Answer = 7.95

  16. Practice • You are interested in how citizens of the US feel about the president. You asked 8 people to rate the president on a 10 point scale. Describe how the country feels about the president -- be sure to report a measure of central tendency and the standard deviation. 8, 4, 9, 10, 6, 5, 7, 9

  17. Central Tendency 8, 4, 9, 10, 6, 5, 7, 9 4, 5, 6, 7, 8, 9, 9, 10 Mean = 7.25 Median = (4.5) = 7.5 Mode = 9

  18. Standard Deviation -1

  19. Standard Deviation 452 58 8 8 - 1 -1

  20. Standard Deviation 58 452 8 8 - 1 -1

  21. Standard Deviation 452 420.5 7 -1

  22. Standard Deviation 2.12 -1

  23. Variance • The last step in calculating a standard deviation is to find the square root • The number you are fining the square root of is the variance!

  24. Variance S2 =

  25. Variance S2 = - 1

  26. Practice • Below are the test score of Joe and Bob. What are their means, medians, and modes? Who tended to have the most uniform scores? • Joe 80, 40, 65, 90, 99, 90, 22, 50 • Bob 50, 50, 40, 26, 85, 78, 12, 50

  27. Practice • Joe 22, 40, 50, 65, 80, 90, 90, 99 Mean = 67 • Bob 12, 26, 40, 50, 50, 50, 78, 85 Mean = 48.88

  28. Practice • Joe 22, 40, 50, 65, 80, 90, 90, 99 Median = 72.5 • Bob 12, 26, 40, 50, 50, 50, 78, 85 Median = 50

  29. Practice • Joe 22, 40, 50, 65, 80, 90, 90, 99 Mode = 90 • Bob 12, 26, 40, 50, 50, 50, 78, 85 Mode = 50

  30. Practice • Joe 22, 40, 50, 65, 80, 90, 90, 99 S = 27.51; S2 = 756.80 • Bob 12, 26, 40, 50, 50, 50, 78, 85 S = 24.26; S2 = 588.55 Thus, Bob’s scores were the most uniform

  31. Review • Ways to “see” data • Simple frequency distribution • Group frequency distribution • Histogram • Stem-and-Leaf Display • Describing distributions • Box-Plot • Measures of central tendency • Mean • Median • Mode

  32. Review • Measures of variability • Range • IQR • Standard deviation • Variance

  33. What if. . . . • You recently finished taking a test that you received a score of 90 and the test scores were normally distributed. • It was out of 200 points • The highest score was 110 • The average score was 95 • The lowest score was 90

  34. 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 • Transforms a distribution of scores so they have a mean of 0 and a SD of 1

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

  36. Z-score

  37. 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

  38. Example • Sample 1: X = 8 = 6 S = 5

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

  40. Example • Sample 1: X = 8 = 6 S = 1.25

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

  42. Example • Sample 1: X = 8 = 6 S = 1.25 Z-score = 1.6 Note: A Z-score tells you how many SD above or below a mean a specific score falls!

  43. 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?

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

  45. Practice

  46. Which challenge did Ross do best? Which did Monica do best?

  47. Practice = 34.6 = 7.4 S = 7.96 S = 2.41

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