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Ch. 10: Summarizing the Data

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- 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.

- 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

- The balancing point in the distribution
- Sum of the scores divided by the number of scores, or

- The most frequently occurring score
- Problem: May not be one unique mode

- Symmetrical (b)
- Asymmetrical or Skewed
- Positively Skewed (a)
- Negatively Skewed (c)

- 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

Variance: Mean of the squared deviations of the scores from its mean

Standard Deviation: Square root of the variance

- 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”

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

- 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.