I'm interested in selecting a sample that is representative of a population. Additionally, I want to be able to quantitatively measure the representativeness of a sample. For example, is there a way to determine, for a sample size n, where n is some fraction of the population size x, how representative the sample is? Can I determine if a given sample is the most representative of a population? What if I introduce weighting of importance for each property? What if the desired representative sample size is 2n or n/2? How would this change the selection?
Are there any resources (textbooks, literature, etc...) that would lead to some relevant statistical measures/tests to answer such questions?