We will begin by drawing samples from a population that has a uniform distribution . In this example, the population distribution shows five levels of a characteristic/variable that were measured in the population. Each level of the variable had the same probability of occurring. The population distribution is presented below.

The scores in the population range from 1 to 5.  The mean of the population is 3.0 and the standard deviation of the population is 1.41 [μ=3.0; σ =1.41].

Our next step is to choose successive samples from this population.