IDL DEMO The IDL demo is organized around the analysis of the New Jersey Pick-It Lottery Data described in "S, An Interactive Environment for Data Analysis and Graphics" by Richard Becker and John Chambers (Wadsworth, 1984). The New Jersey Pick-It lottery is a numbers game. Each ticket costs 50 cents, and gives the purchaser an opportunity to choose a number between 0 and 999. Half the money bet on any particular day is reserved as the prize; the rest goes to the state government. Each day one number is chosen at random, and all those who selected that number share the prize. The data itself consists of two pieces of information, the winning number and the payoff, for each of 254 drawing between May 1975 and March 1976. It is organized as a 254 x 2 data matrix. Two other similar data sets exist (for the drawing between Nov 1976 and Sept 1977 and between Dec. 1980 and Sept. 1981) for later comparison. The first question to address is whether the lottery is fair (i.e. are the winning number uniformly distributed?). This is investigated by producing a histogram or the winning number. <> As you can see the distribution of winning is fairly uniform, which indicates that the lottery is fair. If we were to play would we expect to win on the average? Since each ticket costs 50 cents and there are 1000 numbers, we need an average payoff of 500 dollars to win if we played repeatedly. Again a histogram of the payoffs will help us here. <> The distribution is skew to the right with a few payoffs much greater than $500. We would also like to know what winning numbers were associated with both the big and the small payoffs. This may be investigate with a scatterplot of payoff vs winning number. <> Notice that the outliers all have in common a repeated digit in their winning number. This is readily explained when one discovers that there is a betting option (called a combination bet) in which the player wins if the digits of his chosen number turn up in ANY order (of course he is paid 1/6 th less). However this option demands that no digit be repeated. This is a popular option, hence the prize for a winning number with repeated digits tends to be split among fewer people. Also, winning numbers with leading zeros tend to have high payoffs. O.K., so we are armed and ready to go! Choose a number with repeated digits or one with a leading zero and watch the money roll in. Unfortunately, we are not the only ones who analyze betting records. We have data available for two subsequent time periods. We can compare the overall distribution of payoff for the three time periods via a boxplot display. <> Thus, we find that others have also discovered the secret of maximizing payoff and we are faced with the conclusion that on the average we will not become rich playing the Pick-It lottery. ,¤<5<ø<x´h HELVETICA HELVETICA ?1(DEFAULTFONT 1 (GACHA 10) (GACHA 8) (TERMINAL 8)) ÙgLºiöS²(…â ¾ QLzº