Project Information

Team Captain: Ryan Peng

Team Size: 1

Grade Category: 7-9

Subject Area: Physics/Astronomy/Mathematics

Project Type: Experimental

Language: English

Source of Project Idea:

This project was inspired by the many math contests that I have competed in. These math contests were held on a national or international level, therefore making the prompt scoring of thousands of exam papers impossible without utilizing the multiple choice format. On the other hand, teachers do not like to use the multiple choice format for their exams as multiple choice questions are susceptible to guessing. Teachers are able to use the essay format as they only need to mark a few dozen exam papers. From these observations, I decided to investigate the susceptibility of multiple choice exam questions.

Project Summary:

The purpose of this investigation is to determine, by computer simulation, the distribution of scores obtained on a multiple choice exam. A simulation program was designed, created, and implemented in Microsoft Visual Basic 6.0. Using the simulator, several scenarios were simulated and analyzed.

This project investigated the distributions of scores obtained by a large number of simulated students, who were purely guessing on all of the questions, on various multiple choice exams. The number of questions and the number of answer choices that were on the exam were manipulated. The chances of passing the exam was determined. An expected class average was calculated as well.

The results of the experiment were conclusive. The probability distributions showed that the student wouldn’t be able to obtain a high score on the exam. In some cases, it is possible to pass the exam, but this probability is quite slim! The class average was calculated to be 25% and it is below the passing threshold of 51% (It is assumed that the passing mark is 51%).

In conclusion, it is quite hard to get a passing score on a multiple choice exam by purely guessing. Most likely, the students who are guessing on the answers would fail the exam.

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