Propagation of the Measurement Error and the Measured Mean of a Physical Quantity for Elementary Functions ax and loga x


  • G. G. Rode Institute of Physics, Nat. Acad. of Sci. of Ukraine



propagation of an error, propagation of an uncertainty


Rules have been obtained for the propagation of the error and the mean value for a measured physical quantity onto another one with a functional relation of the type ax or loga x between them. In essence, these rules are inherently based on the Gaussian weight scheme. Therefore, they should be valid in the framework of a real Gaussian weight scheme applied to discrete data of a real physical experiment (a sample). An analytical form that was used to present the rules concerned (“analytical propagation rules”) and their character allow the processing and the analysis of experimental data to be simplified and accelerated.


D.J. Hudson, Statistics. Lectures on Elementary Statistics and Probability (CERN, 1964).

G.G. Rode. Propagation of measurement errors and measured means of a physical quantity for the elementary functions cos x and arccos x. Ukr. J. Phys. 61, 345 (2016).

G.G. Rode. Propagation of the measurement errors and measured means of physical quantities for the elementary functions x^2 and vx. Ukr. J. Phys. 62, 148 (2017).

I.S. Gradshtein, I.M. Ryzhik. Table of Integrals, Series, and Products (Academic Press, 1980).

Propagation of uncertainty [ of uncertainty].

H.H. Ku. Notes on the use of propagation of error formulas. J. Res. Nat. Bur. Stand. C 70, 263 (1966).

Ph.R. Bevington, D.K. Robinson. Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 2002).

J.R. Taylor. An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements (University Sci. Books, 1997).

B.N. Taylor, C.E. Kuyatt. Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results, NIST Technical Note 1297 (National Institute of Standards and Technology, 1994).

P.K. Sinervo. Denition and treatment of systematic uncertainties in high energy physics and astrophysics. In: Proceedings of the PHYSTAT2003 Conference, SLAC, Stanford, Ca, September 8-11 (2003), p. 122.

J. Denker. Nonlinear least squares [].

E.W. Weisstein. Standard Deviation Entry at Math World []

Evaluation of measurement data - An introduction to the "Guide to the expression of uncertainty in measurement" and related documents [ common/documents/jcgm/JCGM 104 2009 E.pdf].



How to Cite

Rode, G. G. (2019). Propagation of the Measurement Error and the Measured Mean of a Physical Quantity for Elementary Functions ax and loga x. Ukrainian Journal of Physics, 64(5), 371.



General physics