We can have, for example, a sample of the states, a sample of Delawareans, or a sample of students taking this class. Two major goals of statistics are to estimate population parameters and to test hypotheses about them. Parameters are usually denoted with Greek letters. Order statistics, however, are denoted with capital letters as in M for median and H l and H u for lower and upper hinges respectively. One purpose of explaining distributions at this point is lay a foundation for the discussion of statistical inference.
Statistical inference involves, among other things, hypothesis testing.
A statistical hypothesis, loosely speaking, is a statement about a population parameter or set of parameters. A hypothesis is tested by applying statistical theory to a sample result. Statistical theory, in turn, depends on probability or theoretical distributions. Frequency distributions show how many observations have various values of the variable. One can thus determine how many cases will be above or below a given point.