Calculate class normal curve in unequal bins?

#1
Hello all,

New here, thanks!

Wanted to ask about finding out my percentile in a class (law school). Our school gives out various bins for grades, e.g. 0-50, 50-55, 55-60, 60-64, 64-68,68-72, 72-76, 76-78, 78-80, 80-85, 85-90, 90-100 and tells us how many students fall in each bin, and what percentage of students that is. So, if you got a 76, it would be really easy to know your percentile (just add the total number of students who did as good or better than you divided by total students, or sum the percentiles above you). However, I wanted to try and create a normal curve over my data. I found a tutorial to do it in excel, but that assumes equally sized bins. I also have a histogram of it in R. In an ideal world, I would like to get the equation for my normal curve so that I could solve for my GPA and see my predicted ranking based on normalcy.

At first I thought this would be useful for my resumes, but it would probably just come across as stupid. Now it's mostly just personal interest. Any advice??

Thanks!
 

obh

Active Member
#2
Hi,

Not sure why do you need a curve ...
I would just create a simple table:
Grade percentages
50 20
55 28
60 31
..........................
90 97
100 100


If you insist n making a bell curve you can try calculating the average and the standard deviation. (x-μ)/σ distribute Z(0,1)
Then you can try using the formula for the normal distribution density.
(it is not exactly normal as it can't be less than 0 or more than 100)
 
#3
Hi obh,

Thanks. We already have a table that we access. The problem is that for me, I'm in the middle of one of the bins. The low end of my bin (76) is 65th percentile. The high end of my bin is 87th percentile. It seems silly, but grades are super important for firms. The difference between being the top 40% of the class and top 20% of the class is huge.

The problem with just a normal curve based on standard deviation is that it's not quite accurate, because the distribution isn't perfectly normal. So maybe rather than a "normal" curve I'm looking for a "best fit" curve.

Does that make sense?