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I have a test containing questions with 3 levels of difficulty:

+------------+------------+-------+
| Question   | Difficulty | Score |
+------------+------------+-------+
| Question 1 | 1          | 100%  |
+------------+------------+-------+
| Question 2 | 1          | 100%  |
+------------+------------+-------+
| Question 3 | 2          |  25%  |
+------------+------------+-------+
| Question 4 | 2          |  75%  |
+------------+------------+-------+
| Question 5 | 3          |  25%  |
+------------+------------+-------+
| Question 6 | 3          |   0%  |
+------------+------------+-------+

Difficulty could mean something like

  1. Beginner
  2. Normal
  3. Expert

The average of the scores is ~54%, but this does not seem fair, because the candidate only answered the easy questions well.

What is the best formula to calculate the final score to reflect the knowledge level of the candidate for 3 difficulty levels? Can we extend this formula to n difficulty levels? What is the method used in education?

Germstorm
  • 101

1 Answers1

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I was wondering that how did u rank the difficulty level of the question? I would suggest to make it an inverse function of average score for that question. for example :- if a question was answered by 4 test takers correctly(100%) and 3 others scored 50% and rest did not attempt then for 10 test taker its weigtage can be 10/(4 + 3*1.5 +0) if all answered it correctly it should be 10/(10) =1 Its just a suggestion , i am not an expert in this field.

Here in my country many national level exams are conducted by third party vendors such as prometric , pearson. and most of them do not disclose their algorithm. so i am not really sure what scaling method is used in education

Anurag
  • 159