March 03, 2006

Surprising Statistic

Writing about web page http://mathstore.ac.uk/articles/maths-caa-series/feb2006/

Imagine a test with 5 questions, where each question is selected randomly from a bank of 10 related alternatives. Some 100,000 different tests can be generated.

Question: How many of these would you need to generate, on average, to have sight of all 50 alternative questions?

Answer: Only 43 (Douglas Adams was one out).

This surprising fact should give pause for thought to an author of online exams concerned about cheating. One of my favourite models for driving learning through assessment is to offer students a number of attempts (say 5) at randomly-generated tests in formative mode before they take the one that counts for credit. In the given example, 10 students colluding could suss out all, or most of, the questions stored in the banks before they take their summative test.


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