We selected five cases from the population shown below. The population is normally distributed, with μ = 5.0 and σ = 2.0. The cases selected are shown in red.

As we can see, the sample does not replicate the population. Only a subset of the population values are contained in the sample. Similarly, the values of scores in the sample are not in the same proportions as they are in the population. This discrepancy between the sample scores and the population values is known as sampling error.