Volume 27 - Article 15 | Pages 419-428

The difference between alternative averages

By James W. Vaupel, Zhen Zhang

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Date received:17 Jul 2012
Date published:12 Sep 2012
Word count:1358
Keywords:covariance, population average, weighting function
DOI:10.4054/DemRes.2012.27.15
Weblink:All publications in the ongoing Special Collection 8 "Formal Relationships" can be found at http://www.demographic-research.org/special/8/
 

Abstract

Background: Demographers have long been interested in how compositional change, e.g., change in age structure, affects population averages.

Objective: We want to deepen understanding of how compositional change affects population averages.

Results: The difference between two averages of a variable, calculated using alternative weighting functions, equals the covariance between the variable and the ratio of the weighting functions, divided by the average of the ratio. We compare weighted and unweighted averages and also provide examples of use of the relationship in analyses of fertility and mortality.

Comments: Other uses of covariances in formal demography are worth exploring.

Author's Affiliation

James W. Vaupel - Max Planck Institute for Demographic Research, Germany [Email]
Zhen Zhang - Fudan University, China [Email]

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