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CHAPTER 4

CHAPTER 4 . Measures of Dispersion. In This Presentation. Measures of dispersion. You will learn Basic Concepts How to compute and interpret the Range (R) and the standard deviation (s) . The Concept of Dispersion. Dispersion = variety, diversity, amount of variation between scores.

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CHAPTER 4

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  1. CHAPTER 4 Measures of Dispersion

  2. In This Presentation • Measures of dispersion. • You will learn • Basic Concepts • How to compute and interpret the Range (R) and the standard deviation (s)

  3. The Concept of Dispersion • Dispersion = variety, diversity, amount of variation between scores. • The greater the dispersion of a variable, the greater the range of scores and the greater the differences between scores.

  4. The Concept of Dispersion: Examples • Typically, a large city will have more diversity than a small town. • Some states (California, New York) are more racially diverse than others (Maine, Iowa). • Some students are more consistent than others.

  5. The Concept of Dispersion: Interval/ratio variables • The taller curve has less dispersion. • The flatter curve has more dispersion.

  6. The Range • Range (R) = High Score – Low Score • Quick and easy indication of variability. • Can be used with ordinal or interval-ratio variables. • Why can’t the range be used with variables measured at the nominal level?

  7. Standard Deviation • The most important and widely used measure of dispersion. • Should be used with interval-ratio variables but is often used with ordinal-level variables.

  8. Standard Deviation • Formulas for variance and standard deviation:

  9. Standard Deviation • To solve: • Subtract mean from each score in a distribution of scores • Square the deviations (this eliminates negative numbers). • Sum the squared deviations. • Divide the sum of the squared deviations by N: this is the Variance • Find the square root of the result.

  10. Interpreting Dispersion • Low score=0, Mode=12, High score=20 • Measures of dispersion: R=20–0=20, s=2.9

  11. Interpreting Dispersion • What would happen to the dispersion of this variable if we focused only on people with college-educated parents? • We would expect people with highly educated parents to average more education and show less dispersion.

  12. Interpreting Dispersion • Low score=10, Mode=16, High Score=20 • Measures of dispersion: R=20-10=10, s=2.2

  13. Interpreting Dispersion • Entire sample: • Mean = 13.3 • Range = 20 • s = 2.9 • Respondents with college-educated parents: • Mean = 16.0 • R = 10 • s =2.2

  14. Interpreting Dispersion • As expected, the smaller, more homogeneous and privileged group: • Averaged more years of education • (16.0 vs. 13.3) • And was less variable • (s = 2.2 vs. 2.9; R = 10 vs. 20)

  15. Higher for more diverse groups (e.g., large samples, populations). Decrease as diversity or variety decreases (are lower for more homogeneous groups and smaller samples). The lowest value possible for R and s is 0 (no dispersion). Measures of Dispersion

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