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A Simple Statistical Estimation of One’s Performance in an MCQ Examination, Based Upon Mock Test Results, Using Binomial Distribution of Probability

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Author(s): Sudipto Roy | Priyadarshi Majumdar

Journal: Open Journal of Statistics
ISSN 2161-718X

Volume: 02;
Issue: 04;
Start page: 452;
Date: 2012;
Original page

Keywords: MCQ | Preparation Index | Knowledge Index | Application Index | Performance Index | Relative Performance | Binomial Probability Distribution | Estimation of Examination Result

ABSTRACT
A simple statistical model is proposed regarding the estimation of one’s overall performance in an MCQ examination along with the calculation of probability of obtaining a certain percentage of marks in the same. Using the data obtained from the results of a sufficiently large number of mock examinations, conducted prior to the main examination, certain parameters quantifying one’s knowledge or preparation for the examination has been calculated. Based on those parameters, the probability of obtaining a certain percentage of marks has been computed using the theory of binomial probability distribution. The dependence of this probability function on various parameters has been depicted graphically. A parameter, called the performance index, has been defined in terms of the expectation value and standard deviation of marks computed from probability distribution. Using this parameter, a new parameter called the relative performance index has been defined. This index estimates one’s performance with respect to the best possible performance. The variation of relative performance index with respect to the preparation index has been shown graphically for different parameter values quantifying various aspects regarding the examination and the examinee.
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