How good is our education system?

--edit-- Since I read about the central limit theorem in a deeper fashion after publishing I have realized that the bell curve is not demanded by statistical laws. This is because exam results are strongly influenced by factors like the amount of effort students put in. The bell curve is still desirable since it allows us to evenly distribute people. -- edit -- 

Exactly how good is our education system? Touted to be a very good one and supported by a few shining gems, what exactly does the data say about the education system?

During the course of this article you will find some pleasant but unexpected things and some expected ones. About the absolutely shocking I cannot make a promise.

First up is my home state Rajasthan. The Rajasthan Board of Secondary Education has been put under the microscope. The choice was simple, this examination board did not ask for anything other than a roll number to get the results of students. Fair enough. I obliged and wrote a Python script to automatically get as many results as possible. After about 30,000 records my Internet connection was ready to die, and so I stopped mining for more results for the day.

While I was processing the results of my mining, I realized that the results of the CBSE class 12 board examinations were declared. With wild glee I prayed that they too ask for nothing more than a roll number. My prayers were granted. After tinkering with the python script a little it was good to go for the CBSE website. Again I put my computer to use and started mining. After about 50,000 results my Internet connection became really slow and computer became really hot. That got my attention and I stopped mining.

Now for the data analysis part. What should I do to this data? A simple answer was to check if it was following the normal curve. What is normal curve you say? Well normal data in simple words is as follows:-

In any population, if you count the frequency of any trait, you will observe a bell like curve

Now this is a very powerful prediction with roots in solid mathematics. Any deviation from this rule implies a bias in the real world where the data was generated. With this in mind I obtained a histogram.

This is the plot for the Rajasthan Board results. The sample size was 30,000 students. Marks obtained vs frequency.
 
There are some interesting things about this plot though.

1. The peak of the bell is not at 50 as expected but at approx 54. This is indicative of a system which inherently passes students who appear for the paper.
2. The slope for the left is steeper for the one on the right. Fewer students seem to be scoring less than the average.

Now for the elephant in the room. Yes, the mammoth spike at 60 surprised me as well. As of now I have been unable to find an explanation for that spike. It is however indicative of something really biased. Some things that caught my eye about it:

• It is HUGE! It is higher than the peak of the curve.
• It is ahead of the curve peak.
• There is no other peak like it.

A spike like that indicates that the system is inherently rigged to provide most students with marks around 60. This is extremely fishy. What is the significance of this number? It is not the fail barrier. Examiners pushing people over the failing marks might have explained such a thing.

This is a skyscraper right in the middle of our marking scheme. One explanation may be that this is some grade demarcation. (this is not confirmed)
Another explanation may be that the sample size was too small. This is less likely as 30k samples for an entire state are enough in my opinion.

 We will talk of this later as I have a conspiracy theory to cook. As soon as the CBSE sample size is noteworthy (arround 1 lakh students) I will plot it's histogram and update this article. Stay tuned.

-- Update -- 1
It seems someone already did this on Quora  for ICSE. Will continue to do for CBSE and pray I have enough data before he does.