Given a data vector x = (x 1, x 2, …, x n ) and a weight vector w = (w 1, w 2, …, w n ), there exist three aggregation schemes in the area of statistics that, under certain assumptions, generate three well-known measures of location: arithmetic mean (AM), geometric mean (GM), and harmonic mean (HM), where it is implicitly understood that the data vector x contains values of a single variable. Among all these three measures, AM is more frequently used in statistics for some theoretical reasons. It is well known that AM ≥ GM ≥ HM where equality holds only when all components of x are equal.
In recent years, some of these three and a new aggregation scheme are being practiced in the aggregation of development or deprivation indicators by extending the definition of data vector to a vector of indicators, in the sense that it contains measurements of development or deprivation of several sub-population groups or measurements of several dimensions of development or deprivation. The...
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References and Further Reading
Hardy GH, Littlewood JE, Polya G (1952) Inequalities. Cambridge University Press, London
Morris MD (1979) Measuring the condition of the world’s poor: the physical quality of life index. Frank Case, London
UNDPÂ (1991) Human Development Report 1991, Financing Human Development Oxford University Press, New York
UNDPÂ (1995) Human Development Report 1995, Gender and Human Development. Oxford University Press, New York
UNDPÂ (1997) Human Development Report 1997, Human Development to Eradicate Poverty. Oxford University Press, New York
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this entry
Cite this entry
Chhetry, D. (2011). Aggregation Schemes. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_109
Download citation
DOI: https://doi.org/10.1007/978-3-642-04898-2_109
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04897-5
Online ISBN: 978-3-642-04898-2
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering