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Practice

Practice. Page 65 2.1. Positive Skew. Note. Slides online. Histogram. Frequency Polygon. Stem-and-Leaf Display. Stem-and-leaf display with a bigger data set Note: The stem-and-leaf is like a histogram turned sideways!. Describing Distributions. Bell-shaped distribution.

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Practice

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  1. Practice • Page 65 • 2.1

  2. Positive Skew

  3. Note • Slides online

  4. Histogram

  5. Frequency Polygon

  6. Stem-and-Leaf Display • Stem-and-leaf display with a bigger data set • Note: The stem-and-leaf is like a histogram turned sideways!

  7. Describing Distributions • Bell-shaped distribution

  8. Describing Distributions

  9. Describing Distributions

  10. Kurtosis • The relative concentration of scores in the center of the distribution • Mesokurtic

  11. Kurtosis • The relative concentration of scores in the center of the distribution • Platykurtic

  12. Kurtosis • The relative concentration of scores in the center of the distribution • Leptokurtic

  13. Measures of Central Tendency • Give one value that represents an entire group of scores • Mean • Median • Mode

  14. Mean • On your tests you get: 70%, 80%, 80%, 90% • The mean is 80% • You know how to do this!

  15. Mean = the mean = an instruction to add (sigma) “the sum of” = a score = the number of scores

  16. Practice • What is the mean of: 5, 8, 6, 3, 2, 2, 9 Mean = 35 / 7 = 5 10.5, 11.6, 12.9, 14.7, 10.5, 11.9, 20.2, 15.5 Mean = 107.8 / 8 = 13.48

  17. Characteristics of the mean • If the mean is subtracted from each score and the differences added, the sum will equal zero

  18. Characteristics of the mean 70, 80, 80, 90 Mean = 80 70 - 80 = -10 80 - 80 = 0 80 - 80 = 0 90 - 80 = 10  = 0

  19. Characteristics of the mean • The mean is the point about which the sum of the squared deviations is minimized

  20. Characteristics of the mean 70, 80, 80, 90 Mean = 80 70 - 80 = -102 = 100 80 - 80 = 02 = 0 80 - 80 = 02 = 0 90 - 80 = 102 = 100  = 200

  21. Population vs. Sample _ x = The mean of a sample  = The mean of a population *They are both calculated the same way!

  22. Population vs. Sample

  23. The Median • The point that divides a distribution of scores into two parts that are equal in size

  24. The Median 10, 5, 13, 6, 14, 17, 2, 6, 9 2, 5, 6, 6, 9, 10, 13, 14, 17

  25. The Median 10, 5, 13, 6, 14, 17, 2, 6, 9 2, 5, 6, 6, 9 10, 13, 14, 17

  26. The Median 5, 8, 9, 15, 20, 25, 50

  27. The Median 5, 8, 9, 15 20, 25, 50

  28. The Median 5, 8, 9, 12, 15, 18, 22, 30, 32, 40

  29. The Median 5, 8, 9, 12, 15, 18, 22, 30, 32, 40

  30. The Median 5, 8, 9, 12,15, 18,22, 30, 32, 40 16.5

  31. Practice • What is the median of: 5, 8, 6, 3, 2, 2, 9 2, 2, 3, 5, 6, 8, 9 (7+1) / 2 = 4 Median = 5

  32. Practice • What is the median of: 10.5, 11.6, 12.9, 14.7, 10.5, 11.9, 20.2, 15.5 10.5, 10.5, 11.6, 11.9, 12.9, 14.7, 15.5, 20.2 (8+1) / 2 = 4.5 (11.9 + 12.9) / 2 = 12.4 Median = 12.4

  33. The Mode • The most frequently occurring score 5, 6, 8, 9, 10, 10, 10, 12, 14, 14 Mode = 10

  34. Practice • What is the mode of: 5, 8, 6, 3, 2, 2, 9 Mode = 2 10.5, 11.6, 12.9, 14.7, 10.5, 11.9, 20.2, 15.5 Mode = 10.5

  35. Determining Skewness

  36. Determining Skewness • For example: Mean = 4 Median = 10 Mean Median

  37. Determining Skewness • For example: Mean = 10 Median = 4 Median Mean

  38. Determining Skewness • Mean < Median = Negative Skew • Mean > Median = Positive Skew • Mean = Median = No Skew

  39. Which should you use?

  40. What is the mean, median, and mode?

  41. Mean = 492 / 38 = 12.95

  42. Mode = 14

  43. (38 + 1)/ 2 = 19.5 Median = 14

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