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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
Years of Education (Full Sample)
0
100
200
300
400
500
600
700
800
900

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
Years of Education (Both Parents w BA)
0
5
10
15
20
25
30
35
40
45
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

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. 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).