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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.

Ch. 10: Summarizing the Data

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### 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

### 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

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

Standard Deviation: Square root of the variance

### 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”

### 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.