Volume 27 - Article 15 | Pages 419–428  

The difference between alternative averages

By James W. Vaupel, Zhen Zhang

This article is part of the ongoing Special Collection 8 "Formal Relationships"

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 - Syddansk Universitet, Denmark EMAIL
• Zhen Zhang - Fudan University, China EMAIL

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