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Quiz about The Mathematics of FunTriviaLike Games

The Mathematics of FunTrivia-Like Games Quiz

I say "Fun Trivia-Like" because of course only the folks at FunTrivia know the exact numbers involved. But if you have a little math savvy, you may enjoy this quiz on, well, quizzes.

A multiple-choice quiz by jbuck919. Estimated time: 6 mins.

Author
jbuck919

Time
6 mins

Type
Multiple Choice

Quiz #
174,324

Updated
Dec 03 21

# Qns
10

Difficulty
Tough

Avg Score
5 / 10

Plays
1625

One at a Time - Single Page - Timed Game

Question 1 of 10

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? Hint

box-and-whisker plot

scatterplot

histogram

leaf-and-stem plot

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Question 2 of 10

2. I now fit a smooth curve to the tops of the bars in my graph of points earned on the x-axis and player numbers on the y-axis. What have I obtained? Hint

A normal distribution

A probability distribution

A bell curve

A uniform distribution

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Question 3 of 10

3. What is the area under the curve of any probability distribution called? Hint

One square unit

It depends on the range of scores

It depends on the number of people playing the game

It cannot be exactly determined but only approximated with a technique from calculus

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Question 4 of 10

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? Hint

The curve is skewed to the left.

The curve has a disconuity between the mean and the median.

The curve is flattened (kurtosis).

The curve is skewed to the right.

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Question 5 of 10

5. This game assigns fifteen points for each correct answer. What is the most likely reason for this? Hint

The number of points needs to be in close mathematical relationship with the number of questions per quiz.

The game masters are allowing for the possibility of assigning half credit in the future.

It gives a greater sense of psychological satisfaction than just awarding one point.

It is much easier to compile results when everything is multiplied by fifteen.

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Question 6 of 10

6. In playing a FunTrivia game, you discover that you make rapid progress through the lower rankings but once you get higher, you can only gain a few ranks per day, if at all. Why is that? Hint

Many players go inactive after a relatively low score

The game masters are making it artificially more difficult to keep you hooked.

After point totals are determined, rank is decided on the basis of who got the score first.

You have played all the quizzes that are easy for you first, and now they are getting harder.

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Question 7 of 10

7. The game has no penalty for guessing on a multiple choice item. "Penalty for guessing?" you say. "How would that work?" Which of these is a way of implementing a penalty for guessing? Hint

You would first be asked to eliminate two choices and then choose your answer from the remaining two.

Every 16th (4 x 4) multiple choice answer would automatically be scored as wrong.

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.

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Question 8 of 10

8. How would adding a great many more randomly selected players change the probability distribution of scores? Hint

The ranges of scores would stay the same but the probabilities would increase.

It would be much harder to advance to the next ranking of player.

The probabilities would stay the same but the score ranges would have to be recalculated.

Shortly after the new players had been "absorbed," the distribution would remain for all practical purposes unaffected.

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Question 9 of 10

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? Hint

There is no reason; it is the result of expected random variation.

As the scores become higher, there are fewer players with a given score.

You are encountering better players, and it's more reasonable that they would be 20 points ahead of you.

You are encountering players who have been playing since scores were given in increments of 20 points instead of 10.

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Question 10 of 10

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 (primarily) wrong with that analogy? Hint

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.

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Quiz Answer Key and Fun Facts

Answer: histogram

The histogram is a kind of frequency distribution. In other words, it shows how frequently or how often each range of scores has been obtained.

2. I now fit a smooth curve to the tops of the bars in my graph of points earned on the x-axis and player numbers on the y-axis. What have I obtained?

Answer: A probability distribution

If I take the area under the curve from, say, a score of 30,000 to a score of 49,990, I can determine the probability that an individual's score lies in that range. Because of the nature of quiz data, it will not look like an inverted bell (a normal distribution is one type of bell curve). It will also not look like a rectangle (a uniform distribution).

3. What is the area under the curve of any probability distribution called?

Answer: One square unit

The area under all probability distribution curves is considered to be one. Among other things, this facilitates calculating probability, which is always a number between zero and one. Lacking the means to draw the curve for you, I can only describe it as rising quickly to a maximum, then trailing off slowly with a long right "tail."

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?

Answer: The curve is skewed to the right.

There is a relatively small number of extremely high scores, which tends to pull the mean up while leaving the median relatively unaffected. Statisticians say that the median is "resistant" to extreme data, while the mean is "nonresistant." By the way, a skew occurs in the direction where the data are sparse (in this case, to the right), not where they are dense.

5. This game assigns fifteen points for each correct answer. What is the most likely reason for this?

Answer: It gives a greater sense of psychological satisfaction than just awarding one point.

You really do feel better when 10/10 gives you a score of 150, don't you?

6. In playing a FunTrivia game, you discover that you make rapid progress through the lower rankings but once you get higher, you can only gain a few ranks per day, if at all. Why is that?

Answer: Many players go inactive after a relatively low score

Low scores are reflective either of players who have low interest or intent players who are only in that range for a short time. Once you leave these players behind, you are mostly up against the comparatively few players who actively play every day and score points as well, thus you have fewer people available to pass and you also need more points to pass each of them.

7. The game has no penalty for guessing on a multiple choice item. "Penalty for guessing?" you say. "How would that work?" Which of these is a way of implementing a penalty for guessing?

Answer: Every wrong answer would result in a fraction off your score.

A guessing penalty is a feature of many standardized exams including the US Scholastic Assessment Test (SAT). It is designed to keep the test taker from benefiting from random guessing.

8. How would adding a great many more randomly selected players change the probability distribution of scores?

Answer: Shortly after the new players had been "absorbed," the distribution would remain for all practical purposes unaffected.

Assuming that the self-selecting body of people who are being added to the list of players is of the same makeup as existing players, the probability of a player falling in any given score range will stay the same.

Answer: As the scores become higher, there are fewer players with a given score.

If you get far enough, you are going to find that only needing 20 more points to advance will be a thing of the past.

Answer: Lotteries are purely games of chance, and the high scorer had to exercise skill to get there.

The difference is admittedly technical. It does not provide much comfort to know that a goal that is for all practical purposes unattainable was in fact won largely through skill and effort rather than a random draw.

Source: Author jbuck919

This quiz was reviewed by FunTrivia editor crisw before going online.
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