## Friday, July 13, 2012

### How long until we "Pig Out"? Part II

In an earlier post, I introduced an activity based on the game . The idea is that participants in the activity will consider ways to answer the question, "How many tosses does it typically take before a Pig Out occurs?"  and then pick one of the ways to explore further. Here, I want to share one of the approaches often selected.

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Experiment
I conducted 100 trials. Tossing the pigs until I rolled a Pig Out constituted a trial. The number of tosses in each trial were collected. I also kept track of how the pigs landed in case I wanted to use the data in a different experiment.

Example
1. pink (no dot)-razorback, pink-razorback, dot-razorback, Pig Out [4]
2. trotter-razorback, pink-trotter, pink-trotter, razorback-razorback, pink-pink, pink-razorback, dot-dot, Pig Out [8]
3. dot-dot, pink-pink, pink-pink, razorback-razorback, Pig Out [5]
4. dot-trotter, razorback-razorback, pink-pink, dot-snouter, pink-pink, razorback-trotter, dot-dot, Pig Out [8]
5. Pig Out [1]
Data
Here are the basic data [number of rolls until a "Pig Out"] for 100 trials
Results
Therefore, based on my experiment, a Pig Out occurs, on average, every 4.68 rolls. The dot plot on the right is another way to represent these results. The plot shows that the mode for the number of rolls until a Pig Out is 1, and I determined that the median is 4. This makes me wonder which average makes the most sense to use in deciding when to pass the pigs.

After completing this experiment, I can see some things that I would change if I were to do it again. In collecting data on how the pigs landed, I did not distinguish between the two pigs. It would be interesting to know if the distribution of rolls between the different pigs was consistent. I also want to go back and look at the scores and determine the average score before rolling a Pig Out. Finally, I wonder if there is another experiment or approach that I could use to check this result.

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This write-up provides a basic model which other participants can use to share their findings. Identifying what represents a single trial is difficult for novices conducting probability experiments, which is why I want a model that defines it and then shows several examples. I also want to introduce the idea of gathering as much data as possible during an experiment. Finally, the example highlights the need to reflect on the results and consider other options.

So how might we verify this result or address some of the other issues raised in this write-up?