Research-based guidance and classroom activities for teachers of mathematics

Fish-Length Distributions

This link takes you to a collection of tasks using Tinkerplots Dynamic Data Exploration on the Key Curriculum website. Fish-Length Distributions is the ninth task on the list.

A fish farmer wishes to validate whether his genetically engineered fish are really growing to longer lengths than his usual fish, as claimed by the suppliers.

The lengths of the sample of new fish can be compared to the old fish, perhaps by inspecting the box plots, but the question remains whether the difference has occurred by chance. Students can explore this by taking their own random samples from the original population to see how likely it is to get lengths of fish as large or larger than those in the sample of new fish.

The task emphasises inference (drawing conclusions about the population of fish), rather than just a description of the samples. The idea that new samples from the same population nevertheless vary by chance is critical to an inferential way of thinking.

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