Analyzing Grade Distribution to Determine Average Grades

[MaxManus]

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.

 

[MaxManus]

Bump
Anyone who knows how to go form course grades to the students average grades?

 

[pmsrw3]

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.

 

[MaxManus]

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:-(

 

[blue_raver22]

I would approach this question by first clarifying what is meant by "normal distribution." In statistics, a normal distribution refers to a specific shape of a bell curve that is commonly used to model data in many fields. It is characterized by a symmetrical shape where the mean, median, and mode are all equal, and the majority of data falls within one standard deviation of the mean.

Based on this definition, if all exams have a normal distribution, it is likely that the average grades of students will also have a normal distribution. However, it is important to note that this is not a guarantee. The average grades could potentially follow a different distribution if there are other factors at play, such as grade inflation or a particularly difficult exam.

Regarding the second question about determining the percentage of students with a certain average grade, it is possible to make some generalizations based on the data provided. For example, if 10% of students received an A as their average grade, it is likely that more than 20% would have a B average, as the majority of students who received an A in one course are more likely to receive an A in another course. However, without knowing the specific grades of each individual student, it is difficult to accurately predict the exact percentage of students with a certain average grade.

In conclusion, while it is likely that the average grades of students will follow a normal distribution if all exams have a normal distribution, it is not a certainty. Additionally, while some generalizations can be made about the percentage of students with a certain average grade, it is not possible to accurately determine this without knowing the grades of each individual student.