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CHAPTER 4

CHAPTER 4. Measures 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. The Range. Range (R) = High Score – Low Score

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CHAPTER 4

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  1. CHAPTER 4 Measures 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.

  2. 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? handout week 3 course Renske Doorenspleet

  3. 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. handout week 3 course Renske Doorenspleet

  4. The Concept of Dispersion • The taller curve has less dispersion. • The flatter curve has more dispersion. handout week 3 course Renske Doorenspleet

  5. Standard Deviation • Formulas for variance and standard deviation: handout week 3 course Renske Doorenspleet

  6. Standard Deviation • To solve: • Subtract mean from each score. • Square the deviations. • Sum the squared deviations. • Divide the sum of the squared deviations by N. • Find the square root of the result. handout week 3 course Renske Doorenspleet

  7. Interpreting Dispersion • Low score=10, Mode=16, High Score=20 • Measures of dispersion: R=20-10=10, s=2.2 handout week 3 course Renske Doorenspleet

  8. 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 handout week 3 course Renske Doorenspleet

  9. 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, less dispersion • (s = 2.2 vs. 2.9; R = 10 vs. 20) handout week 3 course Renske Doorenspleet

  10. 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 handout week 3 course Renske Doorenspleet

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