Make biased dice. Weight (load) dice to favour one of the six numbers. For example, load the number five on both dice so that it is three times more likely to come up than any other face. Test ideas about bias by rolling the loaded dice. Examine the sum of the two numbers rolled. Look at demonstrations of the mathematical principles to analyse the bias. Compare the shape of theoretical data distributions with experimental results. This learning object is one in a series of 11 objects. Three objects in the series are also packaged as a combined learning object.
Key learning objectives
- Students collect and handle data about random events to test conjectures about variation and bias.
- Students interpret frequency graphs to compare experimental results with theoretical probabilities.
- Students compare the shape of theoretical and experimentally derived data distributions in situations where there is bias.
- Students relate the shape of data distributions to statements about sample variation, sample size, and bias.
- Provides scenarios for students to use dice as a means to explore relationships between bias, proportions, sample size, random variation, and statistical distributions.
- Demonstrates that conclusions based on small sample sizes can be incorrect due to random variation.
- Includes scenarios involving a range of even and uneven distributions.
- On-screen tutorials introduce students to mathematical ideas underpinning bias in even and uneven distributions.
- Automatically collates experimental results and displays them as frequency graphs.