The normal distribution can be used to describe the variability existing in thousands, if not millions, of data distributions. Many of these distributions describe everyday quantities, such as the weights of 12-year males in Madison, WI, or the number of inches it snowed in Vail, CO in January during the last 100 years.

Not all data distributions are normally distributed. Some contain more than one peak, and others are skewed (containing a long “tail” on one end of the distribution). For example, the height of humans is bimodal, meaning there are two modes (or peaks) in the distribution. These modes are centered on the average height of males and the average height of females. Another example of a bimodal distribution is the time of day that customers eat at a restaurant. For many restaurants, the distribution would have modes at noon and 7 pm. A skewed data distribution could be constructed by examining the salaries of employees in a corporation. The long tail in the distribution would consist of a relatively small number of employees with very high salaries.

Describe two data sets from your personal life or profession: one that is approximately normally distributed and another that is not normally distributed.

• Describe the data sets, and for the non-normally distributed data set describe its shape (Is it skewed? bimodal?)

For the non-normally distributed data set, what accounts for its non-normal distribution of data?