Scoring of marks, issues

ajayshahane

New Member
Joined
Jul 11, 2010
Messages
12
Hi

Greetings to all.

I am a teacher working in a small educational institute. My institute tests a large number of students – about 100 – every year. Each student gets to write upto 120 tests of about 20 questions each. The tests carry negative marking, as in the student is penalized for incorrect answers.

A typical scoring process is like this:
Marks for each correct answer: +1
Marks for each incorrect answer: –0.25
Marks for questions not attempted: Zero.

E.g. If a student attempted 16 questions, out of which 11 are correct (which means 5 are incorrect), he should be scored as follows:
Correct: 11 * 1 = 11 marks
Incorrect: 5 * (–0.25) = –1.25
Net Score: 11 – 1.25 = 9.75

We enter this into an excel sheet the number of questions attempted and the number of correct questions correctly attempted. When we started out, we used to enter correct answers and total answers in separate cells in Excel sheets. (So the above example would mean cell A1 would contain 11 and A2 would contain 16). Then we used a simple formula to get the net score, displayed in A3.

However this method used too many cells, so we started using a different format:
Correct answers POINT Total Answers. Hence now we use 11.16, which will use only cell A1, (instead of two cells as shown above). Then we extract 16 and 11 separately and display the net score.

We face two kinds of issues
1. Error while entering the data.
a. the data entered in a cell must be of the format CORRECT POINT ATTEMPT i.e. 11.16 as above, but manual errors may lead to entering a data like 16.11, i.e. swapping the two values.
b. the data entered may, by manual error, show more questions attempted than are in the actual test. Each test has exactly 20 questions, but someone entering the data of 11 correct out of 13 attempted may enter 11.31 instead of 11.13

2. Errors while calculating the scores
This is an inherent problem of Excel, I guess. A score of 1 correct out of 5 attempts is entered as 1.05, and should give a net score of ZERO (1*1 – 0.25*4 = 0), but displays a silly message like “-1.11022E-15”. This is true for all scores that should have been ideally reported as ZERO (viz. 2.10, 3.15 and 4.20). Besides an entry with all correct answers, say 7 out of 7, too gets an error message. This too, I suppose is a problem with Excel.

I have pasted the formula hereunder. I’m embarrassed that the formula is not very graceful ;) but this is what we could manage.

Cell A1: (entered scores) 12.13 (meaning 12 correct out of total 13 attempts).
Cell A2: = IF(A1*100>2020,"ERROR",IF(((A1-INT(A1))*100)<INT(A1),"ERROR",INT(A1)-((A1-INT(A1))*100-INT(A1))*0.25))

If you could kindly paste the above two in your excel sheet and then enter 12.12 or 2.10
in cell A1, you will see the problems we face.

We tried =IF(A1*100>2020,"ERROR",IF(INT(A1)>((A1-INT(A1))*100),"ERROR",INT(A1)-((A1-INT(A1))*100-INT(A1))*0.25))

but that gives unreliable scores.

Thank you for your time and patience for reading this elaborate post. Many thanks in advance too, for any help or suggestions. (I understand this is lengthy, hence my apologies too!)

A Shahane
 

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Thank you MGM.

Actually we had started doing something like this, but we quickly aborted it... you can imagine what huge amount of time would be required to manually enter each of the 20 questions, that too for 100 students, for all the tests.... besides, the issue of whether the entry was correct or incorrect actually increases, rather than decreases...

thanks anyway...
 
Upvote 0
This formula in A2 resolves some of your issues. The first IF statement verifies the numbe to the right of the decimal point is not greater than 20 and the second IF statement verifies the number correct is not greater than the number answered. The ROUND function rounds the answer to two decimal places to get rid of the internal calculation error.

Code:
=IF(MOD(A1,1)>0.2,"ERROR",IF(INT(A1)>MOD(A1,1)*100,"ERROR",ROUND(INT(A1)-(MOD(A1,1)*100-INT(A1))/4,2)))

Mike
 
Upvote 0
Many thanks MikeWX.

I found something that I can't figure out the reason of: if I enter 9.09, 5.05 or 3.03 in A1, then A2 displays error, but if I enter 4.04 or 7.07, it works fine.

Otherwise, I think we're home... Your formula is simpler than ours... thanks again.

A Shahane
 
Upvote 0
I think this change in cell A2 will correct those situations and still work for the original issue.

Code:
=IF(MOD(A1,1)>0.2,"ERROR",IF(INT(A1)>ROUND(MOD(A1,1)*100,0),"ERROR",ROUND(INT(A1)-(MOD(A1,1)*100-INT(A1))/4,2)))

Mike
 
Upvote 0
Many thanks Mike Wx for the final solution, ....in case you can, could you explain what was it that was earlier going wrong and you later corrected? This will help us stay clear of such errors in future.
:)
A Shahane...
 
Upvote 0
An internal rounding difference when Excel is calculating MOD(A1,1)*100 results in a value of 2.99999999999998 for the right side of 3.03 instead of a value of 3. By adding the ROUND function, I forced it to result in 3 so it wouldn't consider the number of correct answers as greater than the number of total answers. This also happens with 6.06.

Mike
 
Upvote 0

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