Basic Social Statistics-Lecture02C-Sociology

Measures of dispersion indicate the amount of variation or “average differences” among the scores in a frequency distribution. Variables, Measures of Dispersion, Dispersion, Diversity, Discrete Variable, Qualitative Variation, Range, Average Absolute Deviation, Variance, Standard Deviation, dichotomy, Frequency Distribution, Skewness, Basic Social Statistics, Lecture Slides, Sociology, David Knoke, Minnesota State University (MN), United States of America (USA)

Category: Psycology and Sociology
Subject: Basic Social Statistics
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Published: 23 gennaio 2012
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Chapter 2 Describing Variables 2.5 Measures of Dispersion Measures of Dispersion Measures of dispersion indicate the amount of variation or âaverage differencesâ

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Chapter 2 Describing Variables 2.5 Measures of Dispersion Measures of Dispersion Measures of dispersion indicate the amount of variation or “average differences” among the scores in a frequency distribution. We’re less familiar with such concepts in daily life, although a range of values is sometimes reported: • • • Today’s forecast high temp will be 59-62 degrees N. Korea’s Taepodong missile has a reported range of 2,400 to 3,600 miles Gallup Poll reported 51% of a national sample agree that President Obama is doing a good job, with a “margin of error” of 3% Discrete Variable Dispersion Measures Index of Diversity (D) measures whether two randomly selected observations are likely to fall into the same or different categories D  1 p i 1 K 2 i Higher D indicates the cases are more equally spread across a variable’s K categories (i.e., they are less concentrated) Calculate D for these four GSS regions of residence: Region NORTH EAST pi .175 (pi)2 _________ MIDWEST SOUTH WEST .215 .361 .248 _________ _________ _________ p i 1 K 2 i  _________ D  1  Σ p  _____________________ 2 i The Index of Qualitative Variation (IQV) adjusts D for the number of categories, K K IQV  (D) K 1 IQV gives a bigger “boost” to D for a variable with fewer categories, thus allowing comparison of its dispersion to a variable that has more categories Sally and three friends buy a 12-pack of beer (144 oz.). Ted and seven friends buy two 12-packs (288 oz.). Which distribution of beer is “fairer” (more equally distributed within each set of drinkers)? Sally: 20, 28, 46, 50 oz. Ted: 20, 28, 32, 36, 40, 40, 44, 48 oz. K K   2 IQV   1   pi   K  1  i 1  IQVSally = ___________________________________________________ IQVTed = ___________________________________________________ Indices of Diversity for proportions of U.S. population living in 4 Census regio

Basic Social Statistics-Lecture02C-Sociology

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