Ch. 10: Summarizing the Data

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# Ch. 10: Summarizing the Data - PowerPoint PPT Presentation

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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Presentation Transcript
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.
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
Measures of Central Tendency: The Arithmetic Mean
• The balancing point in the distribution
• Sum of the scores divided by the number of scores, or
Measures of Central Tendency: The Mode
• The most frequently occurring score
• Problem: May not be one unique mode
Symmetry and Asymmetry
• Symmetrical (b)
• Asymmetrical or Skewed
• Positively Skewed (a)
• Negatively Skewed (c)
Comparing the Measures of Central Tendency
• If symmetrical: M = Mdn = Mo
• If negatively skewed: M < Mdn  Mo
• If positively skewed: M > Mdn  Mo
• 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

Standard Deviation: Square root of the variance

Measures of Spread: Variance and Standard Deviation
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

Descriptive Formula

Inferential Formula

Called the “unbiased estimator of the population value”

Variance: Descriptive vs. Inferential Formulas
The Normal Distribution

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

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.