Statistical Analysis for "20 Questions, 4 Answer Choices" Scenario

I chose to do Statistical Analysis on these parameters (20 Questions, 4 Answer Choices) as they are the best choice (out of all 4 scenarios) for creating a multiple choice exam.

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Low Extreme = 0 

Median = Mean of the 100 000^th and 100 001^st elements =  = 5

High Extreme = 15

Mean = , Where E_i is the i^th element of the data set (when arranged from lowest to highest).

Mean =  = 5.009605  (Average Score)

This mean is also the class average (mean). The class average is 25% (Score of 5).

Mode = 5 (It occurs 40222 times.)

Chances of Passing =  = 0.004155 = 0.4155%.

(It is assumed that the passing mark is 51%.)

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