The Mathematics of FunTrivia-Like Games

15 Points Per Correct Answer - No time limit  

1. I label an x-axis with points earned (using ranges of points) and the corresponding y-axis with number of players (again using ranges). I plot one against the other and I obtain a bar graph called a what? scatterplot box-and-whisker plot leaf-and-stem plot histogram

2. I now fit a smooth curve to the tops of the bars in my graph ofpoints earned on the x-axis and player numbers on the y-axis. What have I obtained? A normal distribution A uniform distribution A bell curve A probability distribution

3. What is the area under the curve of any probability distribution called? It depends on the number of people playing the game One square unit It depends on the range of scores It cannot be exactly determined but only approximated with a technique from calculus

4. The mean or average score is higher than the median, which is obtained by ranking the scores and selecting the one in the middle. How does this affect the shape of the curve? The curve is skewed to the right. The curve is flattened (kurtosis). The curve is skewed to the left. The curve has a disconuity between the mean and the median.

5. This game assigns ten points for each correct answer. What is the most likely reason for this? The game masters are allowing for the possibility of assigning half credit in the future. The number of points needs to be in close mathematical relationship with the number of questions per quiz. It is much easier to compile results when everything is multiplied by ten. It gives a greater sense of psychological satisfaction than just awarding one point.

6. In playing this game, you discover that you make rapid progress through the lower rankings but then slow way, way down. What is the reason for this? You have played all the quizzes that are easy for you first, and now they are getting harder. After point totals are determined, rank is decided on the basis of who got the score first. There are few very low scorers but a very large number scoring in the middle range. The game masters are making it artificially more difficult to keep you hooked.

7. The game has no penalty for guessing on a multiple choice item. "Penalty for guessing?" you say. "How would that work?" Every wrong answer would result in a fraction off your score. A "no answer" would get you a fraction of a point, while a correct answer would score zero. Every 16th (4 x 4) multiple choice answer would automatically be scored as wrong. You would first be asked to eliminate two choices and then choose your answer from the remaining two.

8. How would adding a great many more randomly selected players change the probability distribution of scores? It would be much harder to advance to the next ranking of player. The ranges of scores would stay the same but the probabilities would increase. Shortly after the new players had been "absorbed," the distribution would remain for all practical purposes unaffected. The probabilities would stay the same but the score ranges would have to be recalculated.

9. As you advance through the rankings, you notice that the gap between you and the next player is widening, if ever so slightly. It may now take you 20 points to advance rather than 10. What is the reason for that? There is no reason; it is the result of expected random variation. You are encountering players who have been playing since scores were given in increments of 20 points instead of 10. You are encountering better players, and it's more reasonable that they would be 20 points ahead of you. As the scores become higher, there are fewer players with a given score.

10. Hypothetically, this game has 10,000 players, so the probability of being the sole holder of the highest score is 1/10,000. A friend tells you that aspiring to that score is like trying to win the lottery. What is wrong with that analogy? The chances of winning a lottery are a lot less than 1 in 10,000. Lotteries are purely games of chance, and the high scorer had to exercise skill to get there. It only takes a minute to buy a lottery ticket, but a very long time to play all those quizzes. Everybody is smart enough to be the winner, given the time and patience.