How would you analyze this set of data? (exam scores)

I work at palce were we have to score some exams and non of us here are mathematicians so i want to make sure we are doing this right.

I will start by explaining the structure of the exam then, the score scale and finally how we analyze it.

The exam is 10 questions, 2 questions have 1 part and rest wither 3,4 or5 parts. All the questions are fill in questions.

The maximum grade a participant can get for a sing part in a question is 4"fully accurate answer", they will get a 3 if their answers is not fully accurate but "essentially acceptable". 2 is not given to any one and serve as a separator between good performance (ie. Any one who gets 4 or 3) and the poor performance (ie.any one who get 1or 0). Ths score 1 is given for "unacceptable answers" and the score  0 is given to a "very unacceptable answers". Sometimes the nature of any part of any question may no have an answer that would evaluate to a score of 1 for example, so no one will get a score of 1.

We analyze it as follows:
First we score every exam and give the socre based on the scale mentioned above. Then we count how many participants got 4,3,1 and 0 we use pie charts to represent the numbers of participants on percentage  ie. 1out of 100 people got 3 the rest got 4 that woud show as 1% and 99% in the pie chart. This happens for each part of each question.

After that we add up all the scores for all the parts of all the questions for each participants and get their percentage out of 100%. 
We plot this on bar graph along with the average of of all of the participants.

Is there any problems this way of analysis? Is there a better way to do it?

  • Questions at this level should come with a good bounty, otherwise you may not get a response.

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    • Think about how much time it may take someone to write a carefully explained solution, and what a fairly hourly rate for such individual would be. That would help you to decide what a fair bounty should be.

  • At least I need to know if there is a problem or there isn't a problem with the way we analyze it.

  • M F H M F H

    The thing is that it takes already quite some time to read and understand your problem. Also, the last part isn't clear : "we plot this on bar graph..." Also, the question isn't really well defined : there's always a way to do in a better way.... I'll detail in an anwser because it's too long for a comment...

1 Answer

What you do is "OK", you have statistics for each individual (sub)question (which you call "parts") and for the whole exam. Your statistics (and the grading of the exam) obviously does not take into account how the (sub)questions are grouped together, so:

(a) it would be more logical to call (your) "questions" > "part" of the exam, and the "parts" > "question".

(b) an improvement on the statistics would be to also consider how the candidates score for each "question" (what I'd call "part", i.e., group of individual (sub)questions).
[E.g. if these groups correspond to different chapters of the lecture it would show which chapter is globally more or less well understood.]

(c) It's unclear what you mean by "We plot this on bar graph along with the average of of all of the participants." Is it true that you mean : for each individual (sub)question you have bars counting frequency of 0,1,2,3 & 4,  and for the entire exam you have bars counting each possible score, from 0 to 4x(total number of (sub)questions, something around 2 + 8*average(3,4,5) ~ 35) = 140 ?

  • Thank you for taking the time to do this! Really appreciate it.Regarding point C I mean we add up whatever the participants got for the whole exam and devid it by the total possible points *100. Ie. Participants A exam scoore looks like this Questions 1 .........sub questions 1.1 >score 4 .........sub questions 1.2>score 4 .........sub questions 1.3>score 3 Questions 2 .........sub questions 2.1 >score 1 ..etc Sum=4+4+3+1..etc=120.Total possible point=150>(120/150)*100 = 80% is a bar in graph

    • I see that M F H has spent time trying to answer your question and has a raised valid concern. You may want to leave a tip as an appreciation of their time.

  • Each participants has a bar representing their final score.

  • M F H M F H

    Ok, well, of course each participant gets his/her results, but that's usually not considered as part of the statistical analysis.

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