Invariant Relations for Averages in Case of Three Measurement
Keywords:
Classical Averages, Invariant Relations, Average from Three Measurements, Direct Problem of Averages, Reverse Problem of AveragesAbstract
Purpose: The problem of recovery of measurement values based on implicit data is relevant in technical diagnostics when it is impossible to carry out direct measurement and data control. The following five classic averages – arithmetic, geometrical, harmonious, quadratic and counter-harmonious – are often used in technology, science and life. Invariant relations of these averages found earlier have been received for the case of two measurements. The goal of this paper is to deduce on the invariant relations of the given classical averages for the case of three measurements as well as to solve an inverse problem of searching measurements based on known averages. Methods: There have been compiled equation systems; then there has been consecutive exception of unknown variable; consideration of influence of aprioristic information on measurements. Results: Invariant relations have been deduced for each three of five classical averages of three measurements. There have been solved the problem of measurements recovery based on known averages. There have also been solved problems of two types of aprioristic information: whether measurements are members of progression or not. The deduced formulae of measurements recovery by averages formulas are represented in tables. Practical relevance: The deduced invariant relations connecting each three of five classical averages can be useful in technical diagnostics and at processing results of indirect measurements.