The aim of this paper is to discuss different approaches to the quality (or uncertainty) of measurement data considering both historical examples and today's students' views. Today's teaching of data analysis is very much focussed on the application of statistical routines (often called the "Gaussian approach" to error analysis). Studies on students' understanding of measurement however show, that though the majority can be enabled to apply those routines most of the students fail to construct a coherent understanding of the matter. Analysing two historical examples of measurement practice of the time around 1,800 when the statistical approach was established, we point out what often neglected key idea gave rise to the statistical approach to data analysis (the appreciation of randomness in data distribution) and how the emergence of this idea was embedded in a very sophisticated insight on measurement and the nature of measurement data (experimental expertise). These two aspects can vividly be illustrated using the different approaches to data handling of Coulomb and Gauss around the time of 1,800. Gauss's appreciation of the randomness in data distribution consequently led him to other analytical routines as those employed by Coulomb. This is an important aspect concerning the teaching of the statistical routines of data analysis. However, the deep experimental expertise of both Gauss and Coulomb in both cases prevented an application by rote of some routines and shaped their approaches to very successful instruments of data handling. We therefore argue that both the key idea of randomness as well as an elaborated experimental expertise has to be taken into consideration much more than before by instructors and teachers in order to support the students to construct a coherent understanding on the nature and the handling of measurement data and especially the assessment of their quality.