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Using the Characteristics of the Sample Range of Repeated Observations of a Measurand to Estimate Its Numerical Value and Type A Standard Uncertainty Cover

Using the Characteristics of the Sample Range of Repeated Observations of a Measurand to Estimate Its Numerical Value and Type A Standard Uncertainty

Open Access
|Dec 2025

Figures & Tables

Table 1.

Expressions for various estimates of the measurand.

EstimatorsFormulas
Sample mid-range – –
(1)
Mn=ymax+ymin2
Sample mean ––
(2)
y¯n=1nq=1nyq
Median – ⸳ –
(3)
Medn=yn+12,noddyn2+yn2+12,neven
Fig. 1.

Dependence of the efficiency Var of various estimators of the expected value for different PDFs of the observed dispersion of IMI readings: (a) Arcsine; (b) Uniform; (c) Triangular; (d) Normal.

Fig. 2.

Dependence of the ratio of the variances of the sample mid-range and the sample average on the number of repeated measurements n with their uniform distribution law.

Fig. 3.

Dependence of the coefficient α on n for different distribution laws: o – arcsine; ◊ – normal; □ – uniform.

Fig. 4.

Standard hygrometer Testo 400 (a) and humidity generator type “Huminator” (b).

Fig. 5.

Histogram of standard hygrometer readings scatter.

Fig. 6.

Dependence of estimates of the expected value on n: –– arithmetic mean; – – mid-range

Fig. 7.

Experimental dependence (▲) of the conversion coefficient α of the sample range of readings of the standard hygrometer into the sample standard deviation on the sample size n.

Table 2.

Reference hygrometer readings.

№. of observationsWsi [% RH]№. of observationsWsi [% RH]
126.13626.10
226.11726.11
326.12826.13
426.10926.14
526.141026.12
Language: English
Page range: 366 - 370
Submitted on: Aug 25, 2025
Accepted on: Nov 4, 2025
Published on: Dec 23, 2025
Published by: Slovak Academy of Sciences, Institute of Measurement Science
In partnership with: Paradigm Publishing Services
Publication frequency: Volume open

© 2025 Igor Zakharov, Olesia Botsiura, published by Slovak Academy of Sciences, Institute of Measurement Science
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.