The third installment of our little series on statistics is perhaps the most counter-intuitive lesson of all. The lesson is two-fold:
1. A sample only represents the population of interest as a whole if every member of the population of interest had the same chance of being sampled, which is what "random sample" means, regardless of how large the sample is.
2. Given a truly random sample, the accuracy of population estimates based on the sample depends only on the size of the sample, not on the size of the population.
("Sample" is used here to mean a subset of the population available for study, and thus not the population itself.)