Ch 10 summarizing the data
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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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Ch 10 summarizing the data

Ch. 10: Summarizing the Data


Criteria for good visual displays

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

Frequency Distribution Example


Bar graphs example

Bar Graphs Example


Stem and leaf chart

Stem-and-Leaf Chart


Back to back stem and leaf chart

Back-to-Back Stem-and-Leaf Chart


Measures of central tendency determining the median

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

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

Measures of Central Tendency: The Mode

  • The most frequently occurring score

  • Problem: May not be one unique mode


Symmetry and asymmetry

Symmetry and Asymmetry

  • Symmetrical (b)

  • Asymmetrical or Skewed

    • Positively Skewed (a)

    • Negatively Skewed (c)


Comparing the measures of central tendency

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

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


Measures of spread variance and standard deviation

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


Summary data for computing the variance and standard deviation

Summary Data for Computing the Variance and Standard Deviation


Descriptive vs inferential formulas

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


Variance descriptive vs inferential formulas

Descriptive Formula

Inferential Formula

Called the “unbiased estimator of the population value”

Variance: Descriptive vs. Inferential Formulas


Confidence interval for a mean

Confidence Interval for a Mean


Values of x for df 5 for five different confidence intervals

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


The normal distribution

The Normal Distribution

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


Standard scores or z scores

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.


Raw scores x and standard scores z on two exams

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


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