Random Distribution
On a four answer multiple choice question with a large number of test takers, each answer will be selected by 25% of the students, plus or minus 0.75%. The following graph shows 64 sets of this question being answered 10,000 times, for a total of 640,000 answers to each of the four questions, a total of 2,560,000 answers. On only four occasions did the variation from 25% exceed 1% [read: it was either lower than 24% or higher than 26% only four times].
The following three graphs show the effects on distribution of changing the number of questions per set from 100, to 1,000, to 10,000.
Modified Tuesday, November 17, 2009
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