On the Calculation of Mean-Weighted Value in Astronomy

Abstract—Although the calculation of the weighted mean of several individual values (one of the most frequently used operations in scientific analysis) is straightforward, the calculation of the corresponding uncertainty does not always receive the attention it requires. The application of methods of classical statistics to real observational data is often not justified, since the assumptions lying at the basis of these methods are not satisfied. The presence of systematic uncertainties in the averaged measurements and underestimation of the corresponding random errors used to define the weights are typical examples. A new approach to calculating the uncertainty of weighted mean based on a combination of known methods is considered. The proposed method makes it possible to automatically take into account both the random errors and scatter of the input data, making the method suitable for determining realistic errors for mean values in the case of observational data displaying both good and poor consistency. DOI: 10.1134/S1063772913110048 1