Chance and Data:
A Yahtzee experiment.
How likely is it to get 4 or 5 of a kind in 3 attempts of rolling 5 dice?
Stage 3 Statistics and Probability Strand
(NESA, 2019)
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The data
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Data 1 : uses appropriate methods to collect data and constructs, interprets and evaluates data displays, including dot plots, line graphs and two-way tables
Chance 1: students experiment and assign probability of between 0 and 1 as outcomes of their experiments
Mathematical language to be used includes “data”, “survey”, “tabulate”, “vertical axis”, “horizontal axis” and “dot plots” and for chance the language includes “chance”, “event”, “likelihood” and “probability”
Authentic question: Students have been playing Yahtzee and came up with this question as they played the game.
definition of the experiment stays true to the rules of the actual game except that students must "go for" 4 or 5 of a kind.
pre-experiment misconceptions/inferences:
Students believed that yahtzee was "almost impossible".
Students tally their results as either 4 of a kind, 5 of a kind or neither.
Students are assigned a watcher to help maintain accuracy of the experiment
30 students each take 10 turns at Yahtzee. The sample size is 300 turns.
Data from all 30 students is collated in a google sheet.
Students produce tables and graphs from both their individual results and the whole results.
Interpretation and evaluation
Students discuss the data in terms of the most frequent values (the shape of the dot plots)
The probability
Students work out the actual number of each outcomes and the total number in the sample
Students discuss how the overall results are more significant than their individual results. Eg. Students notice that some people got no 4 or 5 of a kind in 10 rolls and some people got 3 yahtzees in their 10 turns.
Students discuss the variance of the results amongst individual students
Assign a probability of between 0 and 1 for both 4 and 5 of a kind
Discuss variable: skill level of the player and how this is mitigated.
Students are asked what they think graphs will look like before they are created.
Look at the theoretical probability of getting a yahtzee (Taylor, 2019) and discuss why our experiment may not have reached theoretical probability (sample size)
Data collection and analysis cycle (Siemon et al, 2015)
Question
data analysis
data representation
conclusions
data collection