chapter 4

CHAPTER 4

Measures of DispersionDispersion = 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.

handout week 3 course Renske Doorenspleet

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?


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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.


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The Concept of Dispersion

The taller curve has less dispersion. The flatter curve has more dispersion.


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Standard Deviation Formulas for variance and standard

deviation:


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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.


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

Years of Education (Both Parents w BA)

0

5

10

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45

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20


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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


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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)


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Measures of Dispersion

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).

chapter 4

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