Does anybody know the origin of the idea of there being a population and a sample? I don't know if this kind of question is okay to ask on this website. 
 A: @NickCox from StackExchange put me onto this page maintained by Jeff Miller on, the "Earliest Known Use of Some of the Words in Mathematics."

Population and sample acquired a statistical colouring in the work of
  Francis Galton and W. F. R. Weldon. In "Typical laws of heredity,"
  Nature, 15, (1877), April 19th, p. 532 Galton wrote, "the population
  ... will conform to the law of deviation [the normal distribution]."
  Weldon applied statistical methods to "samples" of crabs in On Certain
  Correlated Variations in Carcinus moenas, Proceedings of the Royal
  Society, 54, (1893), 318-329.

As suggested by the comments of @whuber and @Kodiologist, the broader notion of learning about a population from a sample is an ancient concept that goes beyond the mathematical, technical use of these particular terms. Notions of learning by experiment are ancient, and perhaps some answer to your question can be found in the history of the scientific method.
A: https://en.wikipedia.org/wiki/History_of_statistics
https://en.wikipedia.org/wiki/Founders_of_statistics
The birth of statistics is often dated to 1662, when John Graunt, along with William Petty, developed early human statistical and census methods that provided a framework for modern demography. 
