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  5. Results of studies of the correlation between the mean, median and midrange for the random observations with the some typical distributions

Results of studies of the correlation between the mean, median and midrange for the random observations with the some typical distributions

M.М. Dorozhovets, O.М. Nykypanchuk
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In the article the results of studies of the dependence of correlation coefficient between the mean, median and midrange from the number of observations with the distributions: Laplaсе, normal triangular, trapezoidal, uniform and arсsine are presented. Studies it is executed by the Monte Carlo method. The number of observations varied from 2 to 100. Besides correlation coefficients the dependences of the selective standard deviations of the mean, median and midrange from the number of observations are also given. On the basis the results of studies it is shown that for all distributions of observations even with the sufficiently large sizes of simples the very close correlation between the mean and median occurs. If the number of observations is about several ten there is also the essential cross-correlation between the mean and midrange, but correlations between median and midrange is smallest. In conclusions the cases when the combined two-element evaluations of the result of measurement as the weighted sum of the mean and median or the mean and median and midrange are should be used is discussed. In such cases for the determination of the standard uncertainty of the weighed result should be considered correlation between these parameters.
Keywords: results, observation, mean, median, midrange, cross correlation