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As it is well known, the standard deviation of a weighted average dependsonly on the individual standard deviations, but not on the dispersion of thevalues around the mean. This property leads sometimes to the embarrassingsituation in which the combined result 'looks' somehow at odds with theindividual ones. A practical way to cure the problem is to enlarge theresulting standard deviation by the $\sqrt{\chi^2/\nu}$ scaling, a prescriptionemployed with arbitrary criteria on when to apply it and which individualresults to use in the combination. But the `apparent' discrepancy between thecombined result and the individual ones often remains. Moreover this rule doesnot affect the resulting `best value', even if the pattern of the individualresults is highly skewed. In addition to these reasons of dissatisfaction,shared by many practitioners, the method causes another issue, recently notedon the published measurements of the charged kaon mass. It happens in factthat, if the prescription is applied twice, i.e. first to a sub-sample of theindividual results and subsequently to the entire sample, then a bias on theresult of the overall combination is introduced. The reason is that theprescription does not guaranty statistical sufficiency, whose importance isreminded in this script, written with a didactic spirit, with some historicalnotes and with a language to which most physicists are accustomed. Theconclusion contains general remarks on the effective presentation of theexperimental findings and a pertinent puzzle is proposed in the Appendix.

On a curious bias arising when the $\sqrt{\chi^2/\nu}$ scaling prescription is first applied to a sub-sample of the individual results