Working with frequencies
Random sequences are interesting in their own right. However, data that is presented in the form of a list is not particularly easy to analyse.
You may have already arranged the results of your spinner experiment into a table of some kind - and our simulation spreadsheet included a simple table to summarise the outcomes.
We find that frequency trees are a useful form of representation to introduce at this stage, especially because they make it easier to develop a narrative - the ‘story’ of the data.
In the picture above, the teacher has recorded data from one group’s experiment as a frequency tree. Each of the four distinct paths through the tree represents a different ‘story’, that the teacher can unpick, as in the following dialogue based a real classroom discussion.
Teacher: Look at the top branches. What’s the story here?
Student: It’s sunny in the morning, and sunny in the afternoon.
T: And how about these two branches? [Indicating the outcome SR]
S: Sunny in the morning, rainy in the afternoon.
T: And these two branches? [RS]
S: Rainy in the morning, sunny in the afternoon.
T: And these? [RR]
S: Rainy in the morning, rainy in the afternoon. Better take an umbrella!
T: So we’ve got four possible outcomes. What are they?
S: Sunny all day, sunny then rainy, rainy then sunny, and rainy all day.
T: Could anything else happen if we stick with this model?
We believe that:
- A dialogue like this helps students to understand both the sequence of events and the tree structure, so that they can be quite sure that all possible outcomes are included.
- Working through the tree structure in the way shown is an important preparatory step before the introduction of the more common (and abstract) probability tree diagrams.
Do you agree?