Friday, October 25, 2013

Securing First Division by Jumping the Bell Curve!

Playing with the Rajasthan Board Exam Results for year 2013 is Fun!! You can certainly do some hair splitting when you've got the result data for almost 2 million students.

Here you'll See, How Students of Rajasthan Board are adept at making it into First or Second Division.

As its clear in plots ( % Marks vs Number of Students), some students have got a special talent of making it into their desired passing division. Everything goes fine in the following graph, it is almost a perfect Bell Curve (Read: Normal Distribution) and as it reaches the threshold marks for getting a First or Second Division, it somehow gets the super normal energy and directly jump over the boundary, and then gets back to normal!

                                            Click on the images to see in a better resolution.

In the 10th Exam plots, Surprisingly the number of students who got 45%, which qualifies them to get a Second Division, is almost ten times of the number of students who are just one mark short at 44.83%.

As they reach 45.17%, everything gets back to normal.

It gets even better when we reach the limit of getting a first division at 60% marks. It seems that all the students who were getting 59.83% are forcibly pushed upwards to get 60% by giving them an extra mark. If it has really been the case, at which stage of evaluation or result processing is this done?

Its not only for the 10th standard exam. The amazing pattern continues for 12th Standard exams of the Rajasthan Board !! See for yourself.

Its tough to understand, how a smooth normal distribution curve, gets a spike and the number of students who have got 59.8% are just 4 while just after 1 mark (0.2%) at 60%, we have got 1,070 students, securing a perfect First Division.

It seems as if the Rajasthan Board has a policy of pushing the students into first and second division by awarding a grace of 1 marks.

After all a lot of Job vacancies require applicants to have a First or Second division to qualify for selection process. Students should either thank their luck or the Rajasthan Board that they are eligible for these opportunities.

Sunday, August 18, 2013

Rajasthan Board Schools: 90-100% in Sessional Marks - Not even 10% in the Board Exam!!

The Complete Result Files (Links to Download the Files):
10th Board: Link
12th Board - Commerce
12th Board - Science
12th Board - Arts

10th Sessional Marks in Schools 
List of Rajasthani Names
It was on Thursday, 6th June 2013 that a friend from my village called me up in the evening and asked if I could check his cousin’s 10th board result. I obliged and tried to access the Rajasthan Board’s result website. Over 1.2 million students had registered for the board exam. The website was not accessible instantly and I had to wait for a few minutes to get the webpage to enter the roll number. I congratulated my friend as his cousin had passed the exam with first division; we chatted a bit more about how our batch was the first one to the get the results online, way back in the year 1999. After a couple of minuted he ringed me again as he wanted to know the results of some other students too. I told him to message me their roll numbers and I shall text him the results after some time as the result website was a bit sluggish.

While checking the results for these students, something caught my attention. A student got more marks in sessionals (20 marks) than the main exam (80 marks) for 3 subjects and he passed the exam with second division marks. I kept on checking the result for the nearby roll-numbers as I wanted to know who has got the highest marks in our school. Most of these students were born in or after 1999; I thought, it has been a long time since I've come out of school and still it seems as if it was just the previous day.

While wondering about the school time memories, I kept on observing that most of the students had got 18 to 20 out of 20 marks in their sessionals while their main exam marks were not even crossing 10 out of 80 marks. 

Next day, I called a friend, who is a teacher in the secondary school. I wanted to know, how these sessional marks are awarded, because in our time, we used to get only 10 marks for sessional exams, which were for the half yearly (mid-term) exams conducted generally in the month of December.

He told me that these sessional marks are a boon for the students and help in improving the results of the school. Out of 20 marks, 10 marks are still for the half yearly exams while remaining 10 marks are a combination of attendance, overall conduct of the student and practical exams, broken into 2 + 3 + 5 marks. As these 20 marks are in the hand of the subject teacher and specially the school. The private schools attract the students and their guardians by promising to give full marks (20 out of 20 marks) in sessionals. Some teachers, especially of government schools, even coerce students to come for tution after school in return of better sessional marks. In the compititive times, where even a single mark can make a difference while applying for admission into universities and for the job openings, these marks are crucial.

I explained to him the 80/20 Pareto Principle, which states that 80% of the output comes from 20% of the action; and it was true even in the case of Rajasthan Board result where a lot of students get more marks in their sessionals than their main exam.

Over the following weekend, I thought of analysing the sessional marks with respect to the overall marks obtained by the students. Afterall sessional marks should be reflecting the learning which happens in the schools, as these are awarded by the schools based on the performance in the mid – term exams and the overall conduct of the stundets.

It was surprising for me that so many students are able to get full marks in their mid-term exams and then perform miserably in their main exams. I thought of checking the result of around 1000 students randomly and see if there is any correlation between the sessionals and the main – exam marks.

I got tired just after checking the result for around 25 students and then felt that its useless exercise, what will I get by doing this? But still it’ll be great if I can download the result automatically. I had read in the newspaper that a student had hacked the ICSE board website and he was able to access the result for all the students by a simple program. I read his post on quora, but didn’t understand it as I didn’t know much of the Java-script.

I thought of doing it by writing a web-query in the MS-Excel, but that was of not much help either. Over the coming few days I browsed the Excel/Java forums and asked a few friends if they could help me in automatically downloading some content by auto-logging into a website with a roll numbr and saving the result page in an excel sheet after parsing it. None of them was willing to help, with an attitude – “yaar ho to jayega, but fight marni padegi!!”

Over next few days I browsed the internet-forums and decided to write a Visual Basic Macro to download and parse the result. I was able to download the result pages as text files for a thousand students but it was difficult to parse the result to analyse it further. It had been a week doing it and there was not much progress in it; so I decided to download the result by MS Visual Basic in an Excel file and parse it by C++.

It was quite thrilling when I saw that I was downloading around 900 students result per minute, parsing it and saving it in an Excel file. Parsing the result was a bit challenging as some of the students had just two subjects displayed in the result page, some of the students result was with held and there were many subjects like Sindhi, Urdu, Sanskrit and I didn’t have much Idea how many key words I had to put to separate the results for these students. Overall It was quite satisfying that I was able to learn Visual Basic and then was able to parse an Excel file by writing a small code in C++.

After downloading the result for 1,207,563 students and taking the results of all those students who had appeared for all six subjects in the exam (1,170,124), I wanted to know if there is any correlation between the sessional marks (out of 20 marks) and the marks obtained in the main exam (Theory – out of 80 marks).

The correlation matrix is shown below:


If we see this matrix, it is quite clear that there is very weak liner correlation between the marks obtained by the students in their main exam (Theory) and the marks given by their schools in their Sessionals. Correlation coefficients whose magnitudes are less than 0.3 have little if any (linear) correlation.

I saw that out of these nearly 1.2 million stundents, there were 253,887 students, whose total marks in their sessionals were more than the total marks in their main exam (theory). For example, some students got 110-120 marks out of 120 marks in their sessionals while 119 or less marks out of 480 marks in their main exam. The correlation between Sessionals and Theory for these students is worse than for all the stundents combined.

The correlation matrix for these students is shown below:


Now what does this mean?

It means that the marks obtained in the sessional, which should be reflective of the students performance in his/her school as assessed by the subject teacher; have no meaningful relation with the marks secured in their main yearly exam. Now there can be a few possibilities – Either the sessional marks are not accurately reflecting the student’s potential or the main exam is not the true measure of the learning students have in their schools. If sessional marks are not reflecting the students’ performances in their schools, then why are these students being given 100+ marks out of 120 marks?

If sessional marks are genuinely assessing the students’ performance in their schools; then the performance in the the schools should have a significant effect on the performance in the main exam. Then, does it mean that going to schools and studying there has no significant relation with the marks students get in the main exam conducted by the Rajasthan Board?

Isn't it unfair for the students who study regularly and do well in their mid-term exams to get good marks while other students who can not even manage 20% marks in their main exam and get over 90% marks in sessionals, most probably just by the grace of their subject teacher and school management?

If we analyse the result further, most of the students who have got 3rd division or just pass marks have crossed the passing line with the help of the marks obtained in their sessionals. 

Even though I strongly believe that the number of marks a student gets in the board exams should not restrict its potential and future prospects, but in the competitive era when the higher education institutions and government is trying to include board marks in the admission criteria, even a single mark can make or break a student’s future.

Some Stats:

Number of students who secured 100 marks in the following subjects:
Hindi -8
English – 11
Science – 374
Social Science -14
Mathematics – 1671

Third Language (Sanskrit, Urdu, Gujrati, Sindhi, Punjabi) – 92

Sunday, January 27, 2013

चिड़ा – चिड़िया और भीगी बिल्ली

पुराने ज़माने में एक चिड़िया अपने आलसी पति चिड़ा के साथ एक गरीब मजदूर के छप्पर में घोंसला बना के  रहती थी। चिड़ा इतना आलसी था की चिड़िया उस से तंग आ गयी थी। वह दिन भर घर पे पड़ा रहता और चिड़िया उसे कुछ काम करने के लिए कहती रहती। एक दिन चिडा अपनी पत्नी के तानों से परेशान होकर उसके साथ चुग्गा ढूँढने चला गया। चिड़िया ने तो इधर उधर उड़ उड़ के काफी सरे चावल इकट्ठे कर लिए, लेकिन चिडा को कुछ मिल ही नहीं रहा था। अचानक उसके खुराफाती दिमाग में मजदूर के घर से कुछ चुराने की गलत सोच आई। वह चुपके से अपने घोंसले पे वापस आ गया और मजदूर के घर से काफी सारी दाल चुरा के अपने घोंसले में रख के सो गया। 

दोपहर में जब चिड़िया चावल ले के घर आई तो उसे काफी गुस्सा आ रहा था । चिड़ा उसे बिना बताये अपने घोंसले पे आकर के सो गया था। चिड़िया ने सोच रखा था की आज वह अपने आलसी पति को खाना नहीं खिलने वाली। लेकिन जैसे ही चिड़िया अपने घोंसले में अन्दर घुसी, उसकी नजर कोने में राखी दाल पे पड़ी। उसका गुस्सा कुछ कम हुआ और उसने बड़े ही प्यार से चिडा को नींद से जगाया। चिडा ने अकड़ के कहा, कभी तो आराम से सो लेने दिया करो, देखो तो सही कितनी मेहनत से इतनी सारी दाल ले के आया हूँ और तुम हो की सुबह से जाने कहाँ गायब हो और इतने से चावल ले कर के आई हो।  चिड़िया बहुत थकी हुयी थी और खाना बनाने की हिम्मत नहीं थी, लेकिन वह चावलों से खीर बनाना चाहती थी इसलिए वह अपनी थकान भूल गयी। चिड़ा ने कहा, खीर कभी और बना लेना, अभी दाल-चावल बनाओ, देखो मैंने कितने दिनों से पेट भरके अच्छा  खाना नहीं खाया है। 

चिडा की जिद के आगे, चिड़िया ने अपना मन मार कर, दाल - चावल बना दिये। वह उन्हें रख कर पास के ही कुए से पानी भरने चली गयी। वह खाना खाने से पहले नहाना चाहती थी। चिड़िया को पानी भर के लाने में कुछ देर हो गयी, इतनी देर तक चिडा को सब्र नहीं हुआ, वह जग कर, बिना मुंह धोये ही खाने के लिए बैठ गया। दाल - चावल इतने स्वादिस्ट बने थे की वह खाता ही गया और खाते - खाते सारा खाना ख़त्म कर दिया। वह इतना सारा खाना खा चुका था की बड़ी मुश्किल से अपने बिस्तर तक पहुंचा, और लेटते ही फिर से सो गया। उसने बर्तनों को फर्श पे ही पड़ा छोड़ दिया। कुछ देर बाद चिड़िया कुए से पानी ले कर आ गयी। वह खुद नहा कर चिडा को नहाने के लिए जगाने गयी, लेकिन वह तो गहरी नींद में था। उसने बड़ी मुश्किल से उसे जगाया और स्वंय रसोई में खाना लेने चली गयी। वहां का नजारा देख कर वह दंग रह गयी। खाने के बर्तन फर्श पे पड़े हुए थे और उनमें कुछ भी नहीं बचा था । वह तमतमाती हुयी चिडा के पास आई और चिल्लाते हुए पुछा - खाना कहाँ गया? 

चिडे ने मासूम सा चेहरा बना के पूछा - क्या हुआ? मैं तो गहरी नींद में था, मुझे क्या पता, तुम ही घर का दरवाज़ा खुला छोड़ गयी होंगी और बिल्ली आकर सारा खाना खा गयी होगी। लेकिन चिड़िया तो चिड़े के जवाब पे विश्वास नहीं हुआ, वह उसे खरी - खोटी सुनाती रही। चिडे ने गुस्से में आकर कहाँ - तुम मुझ पे झूंठे आरोप लगा रही हो, मैं ऐसी जिंदगी जीने के बजाय तो मर ही जाऊं तो अच्छा रहेगा! चिड़िया भी बहुत गुस्से में थी - उसने भी ताव में आकर कह दिया - जाओ, मेरी बला से तो जाकर कुए में कूद जाओ। चिडा और भी ज्यादा गुस्से में आ गया, वह आज चिड़िया को दिखा देना ही चाहता था की वह भी अपनी बात पे अडिग है और कुए की तरफ चल दिया।  

वह कुए पे चढ़ तो गया लेकिन उसमें कूदने की उसकी हिम्मत नहीं थी। वह पीछे मुड़ के देखने लगा की चिड़िया उसे मरने से रोकने के लिए आ रही है या नहीं। लेकिन चिड़िया को पता था की चिडा कहीं कूदने वाला नहीं है, कुछ देर बाद खुद ही वापस आ जायेगा, ऐसा सोच कर रसोई में जाकर फिर से खाना बनाने लगी। उधर, चिडा कुए के किनारे पे खड़ा होकर सोचता रहा की वह कुए में कूदे या नहीं? अगर वह घर वापस चला गया तो उसकी पत्नी उसे फिर से ताने देगी, वह कुछ दिन अपने किसी रिश्तेदार के यहाँ चला जायेगा और वहां भी मेहमानबाजी का लुफ्त उठा कर वापस घर आ जायेगा, तब तक चिड़िया का भी गुस्सा ठंडा हो जायेगा। वह ऐसा सोच ही रहा था की तभी हवा का झोंका आया और वह अपने आप को सम्हाल नहीं पाया, और कुए में गिर गया। 

उसकी "बचाओ - बचाओ" की चीख -  सुन कर आस पड़ोस के चिडे - चिडियाएँ वहां पे इकट्ठे हो गए। उनमें से किसी ने जाकर चिड़िया को बताया की उसका चिडा सचमुच ही कुए में कूद गया है। चिड़िया रोती हुयी - तुरंत ही उड़ के कुए पे पहुंची। वह वहां पे खड़े सभी चिड़ियों से गुहार लगाने लगी की अगर किसी को तैरना आता हो तो वह उसके चिडे को बचाए, लेकिन कोई भी खतरा मोल लेकर यह काम करने को तैयार नहीं था। इतनी सारी चिड़ियों को इकठ्ठा देख के बिल्ली वहां पे धमकी, उसके लिए शिकार करने का इतना अच्छा मौंका कहाँ मिलता। बिल्ली को आते देख वहां से बाकी सारी चिड़ियाये उड़ गयीसिर्फ चिड़िया ही खड़ी रही। उस पे बिल्ली ने जैसे ही झपट्टा मारा वह उड़ कर कुए के दूसरे किनारे पे जा बैठी और बिल्ली से बोली एक चिडा कुए में भी है वह उसे निकाल के खा ले वह पानी में भीगा होने से उड़ भी नहीं सकता। यह बात बिल्ली के दिमाग में भी जम  गयी। वह मेहनत करके वहां बैठी चिडिया को पकड़ के खाने के बजाय भीगे हुए चिडा को खाने के लिए कुए में उतर गयी और जाते ही चिडा को दबोच लिया। वह उसे खाने वाली ही थी तभी ऊपर से चिड़िया ने कहा, इसे भीगा हुआ खाने में क्या मजा आएगा, ऊपर आकर - धूप में बैठ कर आराम से खाना। बिल्ली को भी पानी में भीगने से ठण्ड लग रही थी - उसे धूप मैं बैठ के लंच करने का आईडिया अच्छा लगा। वह चिडे को एक पंजे में दबोच के बड़ी मुश्किल से कुए में लगी रस्सी के सहारे ऊपर निकल आई। उसने बाहर आते ही चिडा को खाने की कोशिश की - इतने में ही चिड़िया ने फिर से कहा, इसे गीला खाने में क्या फायदा - आराम से सुखा करके खाना। बिल्ली बहुत भूखी और थकी हुयी थी लेकिन वह चिड़िया की बातों में गयी। उसने चिडे को अपने पंजे से निकाल के सुखाने रख दिया और खुद फुरफुरी लेकर अपने शरीर से पानी झडाने लगी। वह जम्हाई लेकर अपनी थकान दूर कर रही थी तब तक चिड़ा भी थोडा बहुत सूख गया। चिड़िया ने उसकी तरफ उड़ चलने का इशारा किया। वह भी वहां पे आराम से वेवकूफों की तरह अपने आप को सुखाने लग रहा था। चिड़िया ने खुद ही उसके पास उड़ के जाकर के उसे उड़ चलने के लिए धक्का मारा। इस तरह चिड़िया अपने चिड़ा को वहां से बचा करके उड़ा ले गयी और भीगी बिल्ली देखती ही रह गयी।

मम्मी ने सुनाई यह कहानी :)