I think I got most of this from
Willful Ignorance (Weisberg, 2014) but it was a while since I read it (and this was before I made more detailed notes) so I might be misremembering.
There are what looks like fantastic books on the early days of probability and statistics aside from Weisberg (Ian Hacking is an author that comes to mind, and maybe Stephen Stigler?) but I have not yet taken the time to read them – I'll read more and write something up on this some day.
But statistical understanding is such a recent phenomenon that we have been able to document its rise fairly well[1] which is fascinating in and of itself.
[1]: And yet we don't know basic stuff like when the arithmetic mean became an acceptable way to aggregate data. Situations that obviously (to our eyes) call for an arithmetic mean in the 1630s were resolved some other way (often midrange, mode, or just a hand-picked observation that seemed somehow representative) and then suddenly in the 1680s we have this letter to a newspaper which uses the arithmetic mean as if it was the obvious thing to do and then its usage is relatively well documented after that. From what I understand we don't know what happened between 1630 and 1680 to cause this change in acceptance!