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The American Statistician Volume 38, 1984 - Issue 4
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The Teacher's Corner

Lord's MAD Paradox and Jensen's Inequality

David K. Hildebrand Department of Statistics, University of Pennsylvania, Philadelphia, PA, 19104, USA
Pages 296-297 | Received 01 Dec 1983, Published online: 30 Mar 2012
 
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Abstract

Lord (1983) showed that the mean absolute deviation (MAD) measure of dispersion does not always increase when an additional independent source of random variation is added. Jensen's inequality is used to find necessary and sufficient conditions for this paradoxical behavior. The conditions are unlikely to occur in practice.

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