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How did Bill get a Higher Grade?
Bill got a higher grade when you were both equally prepared?
You both knew the answers to 19 of the 40 questions.
Let’s add up your right marks.
You both got 19 right for sure or a score of 48% on the test.
You discarded 2 of the 5 answers on each question.
That leaves chance to pick a right answer 1 out of 3 times, on-average.
1/3 of the 21 you did know to answer is 7 right from chance, on-average.
19 + 7 = 26 right or a score of 65% on the test, on-average.
Bill and you are not “on-average”.
You each have but one test score.
Bill got lucky with 19 + 9 = 28 or 70%, a low C.
You were not as lucky with 19 + 5 = 24 or 60%, a low D.
Both of you could have received the same grade.
Or, one received a low B and the other an F-.
1 January 2008