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Random or not: open investigations

Description

Test a machine that randomly packages two or three types of fruit jubes: penguin, fish, and frog. Choose the ratio that each jube type is likely to be produced within a packet of 12 jubes. For example, choose a 2:1 ratio so that penguin jubes are twice as likely to be produced as fish jubes. Look at numbers of the most common jube type, patterns in sequences of one jube type, or alternating sequences of jube types. For example, look at patterns such as penguin, fish, penguin, fish (alternating run of 4). Analyse the results of large samples. Compare the numbers of the most common jubes or longest runs of jube types. Identify the most likely number of the most commonly occurring jube type or the longest run most likely to occur in a packet. This learning object is one in a series of 17 objects.

Key learning objectives

  • Students observe and analyse data about random events to test conjectures about variation.
  • Students interpret frequency graphs illustrating experimental results.
  • Students observe the shape of experimentally derived data distributions.
  • Students relate the shape of data distributions to statements about sample variation and sample size.  

Educational value

  • Provides sampling scenarios for students to explore relationships between proportions, sample size, and random variation in even and uneven distributions.
  • Demonstrates that conclusions based on small sample sizes can be wrong due to random variation.
  • Automatically collates experimental results and displays them as frequency graphs.