IPS - Day 3

Today we wrapped up our look into theoretical and experimental probability. We opened with a discussion of the similarities and differences between the rolling die and tossing hair clip experiments. This lead to a discussion of the "Law of Large Numbers" and the fallacious "Law of Averages."  Examples were provided, such as an athlete having a hot hand or being due to score. An explicit connection was made between experimental and theoretical probability. For students who had pre-calculus or calculus, you can relate this to a limiting process. A few additional examples were provided to help reinforce the idea.

Next, another experiment was conducted by tossing a coin 100 times. As before, students were asked to consider what they thought would happen. The number of heads minus the number of tails becomes the response variable that is measured. I had students put these values up on the board along with the longest streak of heads or tails that was tossed. Most students expected to see heads and tails within 4 or 5 of each other. They were surprised to see one student had tossed 38 heads and 62 tails. Another student had 58 heads and 42 tails. These exceeded what students thought might happen. The length of streaks was also surprising to students. Many thought 3-5 would be the length of the longest streak but there were many that were 10 or more, including one that was 15 and another that was 13.

This was an opportunity to introduce the idea that the data we gathered was random data and that randomness often looks quite different from what our mind conceives. I used this as an opportunity to mention that statistics looks at random data that we generate and compares it to our understanding of what random data should look like. If the two mesh then everything is fine, but if the two don't mesh we need to understand what is at play to cause the difference.

We finished with playing a coin tossing game. Again, students set down expectations before playing. They were surprised at the percentage of games that were won by a 4-1 split versus a 3-2 split.

For reflection, students considered connections between theoretical probability, experimental probability, and the "Law of Large Numbers." They were also asked to state the law in their own words and provide an example.

Visit the course notes for the day to read a student's perspective about the class and see the day's slides.