Download Random Basic Advanced.nlogo (30 KB)
Random Basic Advanced is authored in the NetLogo modeling-and-simulation environment. The model is part of ProbLab, a curricular unit designed to enrich student understanding of the domain. The online unit package will include a suite of models, student worksheets, and a teacher guide. Below is an applet of 'Random Basic Advanced.' You can interact with this model by pressing the buttons and changing the slider values to run this model under different settings. You may want to slow down the model in order to get to know it -- use the ADJUST SPEED slider that is on the top-left corner of the graphics window. Note that this model is still under development and is yet to undergo our rigorous checkout procedure.
Gist
Random Basic Advanced extends on the ProbLab model Random Basic. In that model, there is only a single "messenger," the dart-shaped creature that builds up bricks. In Random Basic Advanced you can still work with a single messenger, but you can also work with 2, 3, or more. The model explores the effect of sample size on the distribution of sample mean. The larger the sample size, the smaller the variance of the distribution. That is, the sample space does not change, but extreme values become more and more rare as the sample size increases. Combinatorial analysis helps understand this relation.
Run the model with NUM-MESSENGERS = 1. Compare the histogram in the plot to the towers in the graphic windows. What do you see? Now setup and run the model with NUM-MESSENGERS = 2. Is the histogram any different from before? Repeat this for values of NUM-MESSENGERS 10, 20, and 30. For a sample size of 1, the raw data (the bricks in the towers) are exactly the same as the histogram. For a sample size of 2, we begin to see a certain shallow bump in the middle of the distribution. For larger sample sizes, this bump becomes more and more acute. For a sample size of 30, the distribution is narrow.
Questions to Ponder
What is the standard deviation dependent on? For a fixed number of messengers, would a larger sample space change the standard deviation? If so, why? For a fixed sample space, should a change in the number of messengers affect the standard deviation? If so, why? Can you determine a relation between these three values (NUM-MESSENGERS, SAMPLE-SPACE, and STD-DEV)?
Once the model has run for many trials, should the BIGGEST-DIFFERENCE, the vertical difference between the tallest column and the shortest column, increase or decrease? On the one hand, individual columns have "opportunities" to get very tall, but on the other hand, all columns have the same opportunities. Is this a paradox?
[last updated April 12, 2005]