Analyzing Grade Distribution to Determine Average Grades

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SUMMARY

The discussion centers on the relationship between individual course grades and overall student averages, specifically addressing whether average grades will follow a normal distribution if course grades do. It concludes that without knowing which student received which grade, one cannot definitively determine the average grade distribution. The correlation between grades in different courses exists but is not perfect, indicating that assumptions about average grades based solely on course distributions are unreliable.

PREREQUISITES
  • Understanding of statistical distributions, particularly normal distribution.
  • Familiarity with grade correlation concepts across different courses.
  • Basic knowledge of data analysis techniques for educational performance.
  • Experience with interpreting grade distributions in academic settings.
NEXT STEPS
  • Research "Statistical Correlation in Educational Data Analysis" to understand grade relationships.
  • Learn about "Bayesian Inference" for making predictions based on incomplete data.
  • Explore "Data Visualization Techniques" to represent grade distributions effectively.
  • Investigate "Regression Analysis" to model the relationship between course grades and overall averages.
USEFUL FOR

Students, educators, and data analysts interested in understanding grade distributions and their implications for academic performance evaluation.

MaxManus
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If all the exams have normal distribution will the average grades to student also be normal distributed?

I have data on how many got which grade in every course I have taken, but I want to know how many have A, B, C,..,E average. The problem is that I don't know which student got which grade, but it is safe to assume that the students who got an A in course xxx are more likely to get an A in course yyyy than the students who got an E in course xxx.

Is it possible to say something about the percentage who got A in average when you have the data I have?
If 10 percent got A, 20 B, 30 C, 20 D, 10 E, on average will more/less than 20 percent have B average?

English is not my native language so please ask if you do not understand the question.
 
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Anyone who knows how to go form course grades to the students average grades?
 
MaxManus said:
If all the exams have normal distribution will the average grades to student also be normal distributed?
There is no really good reason to expect that. The distribution of grades for many students in one course has to do with differences between the students. The distribution of grades for one student in many classes has to do with differences between the classes. The nature of differences between the students tells you nothing about differences between the classes.

I have data on how many got which grade in every course I have taken, but I want to know how many have A, B, C,..,E average. The problem is that I don't know which student got which grade, but it is safe to assume that the students who got an A in course xxx are more likely to get an A in course yyyy than the students who got an E in course xxx.

Is it possible to say something about the percentage who got A in average when you have the data I have?
Not without more information (or making some assumptions). You expect, as you say, that there will be some correlation between grades for different courses. But the correlation won't be perfect. The answer to your question will depend on the correlation.
 
pmsrw3 said:
There is no really good reason to expect that. The distribution of grades for many students in one course has to do with differences between the students. The distribution of grades for one student in many classes has to do with differences between the classes. The nature of differences between the students tells you nothing about differences between the classes.

Thanks I didn't think about that there are two different differences.

Not without more information (or making some assumptions). You expect, as you say, that there will be some correlation between grades for different courses. But the correlation won't be perfect. The answer to your question will depend on the correlation.

I have only the grade-distribution for each class:-(
 

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