611 – Using Data Sets, Technology, and Activities to Teach Statistics
Powerball: A Wealth of Data for a Variety of Student Projects
Edward Mansfield
The University of Alabama
Be a winner with Powerball! Use their data to expand the experience and creativity of your students in analyzing data. Since the lottery game Powerball started in 1992, changes have been made that have altered the probability of winning the grand prize. The basic process of drawing five white balls from one bin and one red ball from a different bin has remained constant, but changes in the number of balls in each bin has occurred. Data for all drawings is readily available on the internet and also provided by the author in an edited form. Some activities: Ask students to determine which numbers are more likely or less likely to occur. Obviously all numbers are equally likely, but students may find some “hot� and “not� numbers due to changes in the game rules over time and by their looking only at default histograms. Examine the distribution of discrete order statistics. Model the changing size of the jackpots over time. Determine the breakeven point for the jackpot. Analogies are given to help one understand how unlikely it is to win the big prize. When additional numbers are added to alter the probability of winning, the higher numbers will have lower frequencies when compared to older data because they have been available for fewer drawing. The reason may not be obvious to some students. Can the distribution of the discrete order statistics be determined from the data? How should the parameters of the distributions be estimated?
