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Ch. 10: Summarizing the Data

Ch. 10: Summarizing the Data. Criteria for Good Visual Displays. Clarity Data is represented in a way closely integrated with their numerical meaning. Precision Data is not exaggerated. Efficiency Data is presented in a reasonably compact space. Frequency Distribution Example.

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Ch. 10: Summarizing the Data

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  1. Ch. 10: Summarizing the Data

  2. Criteria for Good Visual Displays • Clarity • Data is represented in a way closely integrated with their numerical meaning. • Precision • Data is not exaggerated. • Efficiency • Data is presented in a reasonably compact space.

  3. Frequency Distribution Example

  4. Bar Graphs Example

  5. Stem-and-Leaf Chart

  6. Back-to-Back Stem-and-Leaf Chart

  7. Measures of Central Tendency: Determining The Median • Arrange scores in order • Determine the position of the midmost score: (N+1)*.50 • Count up (or down) the number of scores to reach the midmost position • The median is the score in this (N+1)*.50 position

  8. Measures of Central Tendency: The Arithmetic Mean • The balancing point in the distribution • Sum of the scores divided by the number of scores, or

  9. Measures of Central Tendency: The Mode • The most frequently occurring score • Problem: May not be one unique mode

  10. Symmetry and Asymmetry • Symmetrical (b) • Asymmetrical or Skewed • Positively Skewed (a) • Negatively Skewed (c)

  11. Comparing the Measures of Central Tendency • If symmetrical: M = Mdn = Mo • If negatively skewed: M < Mdn  Mo • If positively skewed: M > Mdn  Mo

  12. Measures of Spread:Types of Ranges • Crude Range: High score minus Low score • Extended Range: (High score plus ½ unit) minus (Low score plus ½ unit) • Interquartile Range: Range of midmost 50% of scores

  13. Variance: Mean of the squared deviations of the scores from its mean Standard Deviation: Square root of the variance Measures of Spread: Variance and Standard Deviation

  14. Summary Data for Computing the Variance and Standard Deviation

  15. Descriptive vs. Inferential Formulas • Use descriptive formula when: • One is describing a complete population of scores or events • Symbolized with Greek letters • Use inferential formula when: • Want to generalize from a sample of known scores to a population of unknown scores • Symbolized with Roman letters

  16. Descriptive Formula Inferential Formula Called the “unbiased estimator of the population value” Variance: Descriptive vs. Inferential Formulas

  17. Confidence Interval for a Mean

  18. Values of x (for df =5) for Five Different Confidence Intervals

  19. The Normal Distribution Standard Normal Distribution: Mean is set equal to 0, Standard deviation is set equal to 1

  20. Standard Scores or z-scores • Raw score is transformed to a standard score corresponding to a location on the abscissa (x-axis) of a standard normal curve • Allows for comparison of scores from different data sets.

  21. Raw Scores (X) and Standard Scores (z) on Two Exams

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