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March, 1948 Approximate Weights
John W. Tukey
Ann. Math. Statist. 19(1): 91-92 (March, 1948). DOI: 10.1214/aoms/1177730297

Abstract

The greatest fractional increase in variance when a weighted mean is calculated with approximate weights is, quite closely, the square of the largest fractional error in an individual weight. The average increase will be about one-half this amount. The use of weights accurate to two significant figures, or even to the nearest number of the form: 10, 11, 12, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 50, 55, 60, 65, 70, 75, 80, 85, 90, or 95, that is to say, of the form $10(1)20(20)50(5) 100 \times 10^r$ can thus reduce efficiency by at most $\frac{1}{4}$ percent, which is negligible in almost all applications.

Citation

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John W. Tukey. "Approximate Weights." Ann. Math. Statist. 19 (1) 91 - 92, March, 1948. https://doi.org/10.1214/aoms/1177730297

Information

Published: March, 1948
First available in Project Euclid: 28 April 2007

zbMATH: 0041.25901
MathSciNet: MR24109
Digital Object Identifier: 10.1214/aoms/1177730297

Rights: Copyright © 1948 Institute of Mathematical Statistics

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Vol.19 • No. 1 • March, 1948
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