People have been collecting and using data for much longer than we've had fancy mechanisms of analyzing it. The Census goes back to 1790, as one example. Still, in most of my own experience, I've only ever seen this data presented in the form of long tables or the like.
If anyone has anything to offer, I'd also be curious about the use of data visualization in historiography.
There were plenty of data visualizations pre-computer. Many of our standard visual tropes for graphs and graphics come from William Playfair (1759-1823): the bar chart and the pie chart in particular, but probably others (he is particularly well-known for this time-series chart but I don't know if he initiated the genre).
The use of cartograms (map data) was common by the 19th century though the principles of use (e.g., how to use them without being misleading) were not completely standardized until the early 20th century. So William Z. Ripley, for example, a racial theorist and cartographic theorist, was writing articles about the need to make sure that complex maps of human difference were done in standardized and honest ways. This sort of thing was commonly discussed by statisticians.
This is not a full answer; it is just an exhortation to look deeper! This is a massive topic. A very enjoyable overview of pre-computer data visualization is found in Edward Tufte's The Visual Display of Quantitative Information (which is not a history book, but uses reference to historical visualizations). Computer-aided data visualization is actually very recent!
