Analytical Probability, Averages and Data Distributions in the 19th Century

It was in the offices of administrative statistics that data work was held in the nineteenth century, where the most massive amount of numerical information was processed. Reconstructing the know-how of this era leads to the formation of the theory of the average and its international dissemination. Indeed, it not only governed the calculations but also the organization of these offices. Once sealed in the work of the astronomer Adolphe Quetelet and promoted internationally, mainly in Europe, this theory of the average became the key to the statistical know-how of that century. It went hand in hand with presuppositions on the dispersion of observations today considered as obsolete. We can therefore put an end to the legend of the universality of the law of large numbers.