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Over the past few days, I've expanded this article, including the addition of new sections and external links. The prior version of the article was largely unreferenced and was written in an unencyclopedic tone. It also placed undue weight on the minor occupations that Lexis worked at during the years before he began his notable work. Regarding the work itself, the prior version placed undue weight on the naming of the Lexis diagram, and did so in a point-of-viewish fashion.
Two specific points of note: I removed both of the (undocumented) references to Lexis being the "founder" of the study of insurance. Given that the insurance business had existed for more than a century before Lexis came around, this seemed an outlandish claim. I also noted that the date of death given in the MacTutor biography does not agree with the dates given in the German sources. I replaced the MacTutor date with the German-sourced date (and I did this in the Wikidata listing, as well).