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On Rounding Percentages

Persi Diaconis and David Freedman
Journal of the American Statistical Association
Vol. 74, No. 366 (Jun., 1979), pp. 359-364
DOI: 10.2307/2286335
Stable URL: http://www.jstor.org/stable/2286335
Page Count: 6
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On Rounding Percentages
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Abstract

We assess the probability that a table of rounded percentages adds to 100 percent. This extends work of Mosteller, Youtz, and Zahn (1967) who found that the chance of rounding to 100 percent was about 3/4 with three categories, 2/3 with four categories, and (6/π c)1/2 with a large number c of categories. We give a mathematical treatment of this phenomenon when the table is drawn from a multinomial distribution or from a mixture of multinomial distributions. We discuss the very different small-sample behavior and treat Benford's leading digit data as an example.

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