Scientific Journal of KubSAU

Polythematic online scientific journal
of Kuban State Agrarian University
ISSN 1990-4665
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Orlov Alexander Ivanovich

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Bauman Moscow State Technical University

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Articles count: 123

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abstract 1341710070 issue 134 pp. 853 – 883 29.12.2017 ru 50
According to measurement theory, statistical data are measured in various scales. The most widely used ordinal scale, scales of intervals and relations. Statistical methods of data analysis should correspond to the scales in which the data is measured. The term "correspondence" is specified with the help of the concepts of an adequate function and an allowable scale transformation. The main content of the article is a description of the average values that can be used to analyze data measured in the ordinal scale, interval and relationship scales, and some others. The main attention is paid to the means for Cauchy and the means for Kolmogorov. In addition to the mean, from this point of view, polynomials and correlation indices are also analyzed. Detailed mathematical proofs of characterization theorems are given for the first time in scientific periodicals. It is shown that in the ordinal scale there are exactly n average values, that can be used, namely, n order statistics. The proof is represented as a chain of 9 lemmas. In the scale of intervals from all Kolmogorov means, only the arithmetic mean can be used. In the scale of relations from all the Kolmogorov means, only the power means and the geometric mean are permissible. The kind of adequate polynomials in the relationship scale is indicated