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. Observed distributions will only approximate these shapes. Although we will look at the normal distribution more closely next week, for now notice that it has the properties, which incidentally further clarify the meaning of the standard deviation. About 95 percent fall between plus and minus two standard deviations of the mean. Another symmetric distribution is called rectangular.