Analyzing Grade Distribution to Determine Average Grades

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Discussion Overview

The discussion revolves around the relationship between individual course grades and overall average grades among students, specifically whether the average grades can be inferred from the distribution of grades across multiple courses. Participants explore the implications of grade distributions and correlations between courses.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions if average grades will also follow a normal distribution if all course grades do, suggesting that the relationship is not straightforward due to differences between students and classes.
  • Another participant notes that while there may be a correlation between grades in different courses, this correlation is not perfect, and more information or assumptions are needed to make definitive statements about average grades.
  • Concerns are raised about the lack of data on which specific students received which grades, complicating the ability to determine average grades from the provided distribution data.
  • One participant acknowledges the complexity of the differences between students and classes, indicating a realization of the nuances involved in the analysis.

Areas of Agreement / Disagreement

Participants generally agree that the relationship between course grades and average grades is complex and that assumptions or additional information are necessary to draw conclusions. However, there is no consensus on how to approach the analysis given the available data.

Contextual Notes

Participants express limitations in their data, specifically the absence of individual student grades, which affects their ability to analyze average grades accurately. The discussion highlights the dependence on assumptions regarding correlations between grades across different courses.

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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