need help with certification practice exam grading formula

Question

Since i'm being trolled with negative marks on my post without people even giving any kind of constructive feedback, other than Rolazaro, I'm re-writing the question:

I am creating a program for a friend of mine that runs a technical college to write / practice / take exams for certifications and other tests. My problem is that I am not very mathematically inclined and need help with the formula for calculating the point average for each question based on three factors:

• the difficulty of the question (values 1-10, 10 being hardest)
• the total number of questions in the test (between 10 to 250+)
• the total points possible, regardless of the number of questions (1,000 points)

The problem that i'm having is that I cannot find a way to factor in two of the variables so that the total possible score will always be 1,000:

• the total number of questions on the test (let's call it "Qi", (i) represents the question #)
• the difficulty rating of the question (let's call it "D")

Can anyone PLEASE help me with this? I really am struggling to figure out a formula for this...

Answer 1

Ok, sorry everyone.

It seems that my difficulty was all due to a mistake I made on my excel sheet calculation.

My original error with the 1250/1000 was due to my having missed multiplying the student score (1250) by the point average, which was calculated by the sum of the question difficulties divided by 1,000 - which for 1250 would give me about ~0.8.

After summing up the difficulty ratings of correctly answered questions (for example, 1020) and multiplying by 0.8 - it would give me the correct score out of a total 1,000.

1000/1250 = 0.8 point average
1020 sum of student's correct question difficulties
1020*0.8 = 816 of 1000 final score, or 82% when up-rounded