Calculate Average of Top 5% of Biology Test Scores

[kankerfist]

I have some statistics on a test from my biology class and I was wondering if there is enough information provided by the stats to be able to calculate the average of the top 5% of scores. I have used a graph in mathematica to get a pretty good idea of what the top 5% average is, but I was wondering if anybody had any ideas on figuring this out. I've attached a jpg of the stats. Thanks a lot

 

[HallsofIvy]

According to your graph you have 250 scores so the top "5%" would be the top 12.5 scores. The only information shown is that 5 are between 90 and 100 (actually, it also says "highest grade 90" so presumably all 5 of those are 90) and 44 are between 80 and 90. Obviously, then, the top 12 are between 80 and 90, probably averaging close to 90, but without more precise information nothing more can be said.

 

[Architeuthis Dux]

Thank you for providing the statistics from your biology test. To calculate the average of the top 5% of scores, we would need to know the total number of scores and the actual scores for each student. It is not possible to accurately calculate the average based on the information provided in the graph alone.

In order to calculate the average of the top 5% of scores, we would first need to determine the cutoff score for the top 5%. This can be done by multiplying the total number of scores by 0.05 (5%). For example, if there are 100 scores, the cutoff score for the top 5% would be 100 x 0.05 = 5. This means that the top 5% of scores would be any scores above 5.

Once we have determined the cutoff score, we can then calculate the average of the top 5% of scores by adding up all the scores above the cutoff and dividing by the number of scores in the top 5%. For example, if there are 100 scores and the cutoff score is 5, we would add up all the scores above 5 and then divide by 5 to get the average.

Without knowing the actual scores for each student, it is not possible to accurately calculate the average of the top 5% of scores. However, using the graph in Mathematica can give you a rough estimate of the average. I would suggest obtaining the actual scores and using the method described above to calculate the average of the top 5% of scores for a more accurate result.