# Guest Blog: Scaling of Marks in NEET,NBE or DNB Exams

**Understand How Scaling of Marks is Done in NEET DNB and NBE Exams and hence how to attempt these online Papers.**

Students often come across the term scaling in consideration of examinations with multiple question papers, and get confused. All know that scaling plays an important role in the final result of an examination, yet it remains unclear to many how the actual result is achieved.

The following article is a short summary on how NEET PG, DNB and other online exams are graded, when there are multiple set of question papers. The explanation is a bit technical and hence requires understanding of probability and statistics

The evaluation of the exam papers are based a process we call as ITEM Response Theory. This can be made clear with the following example.

Suppose in a test of 10 Questions each correct question carries 4 Marks and each incorrect attempt is -1 Marks and Zero Marks for each unattempted question.

Now with the classic Evaluation Theory the students are graded according to the total marks out of 40 achieved by them.Moreover, each question even though their difficulty level is different would carry the same marks, implying similar marks for both easy and tough questions and hence no rewards for answering a difficult question correctly. The final result would then be calculated on the test as whole with no regards to the difficulty critera in the examination paper. Such type of evaluation theory works well when all students have the same set of questions, but fails when there are multiple set of question paper, as in the latter it becomes necessary to factor in the difficulty level of the students to evaluate their respective proficiency

Hence we have ITEM response mechanism to incorporate the difficulty level and multiplicity of exam papers It is an age old (More than 50 Years )statistically proven and accepted model . And hence it is fair to all (Unlike the perception among students and various teachers)

Understanding this model can also benefit in attempting pattern in exam.

**Now in ITEM Response Model each question has a different weightage and hence getting correct /incorrect or leaving the question will give you a different score which is popularly called Scaling of Marks.**

Each question which appears in such a Online Test has associated two parameters ** attempt % and accuracy %** which determines the overall difficulty level of the question.

** Attempt % in Scaling of Marks**

How many students who saw that particular question actually ended up attempting the question.

So suppose out of 100 students who saw the question (During the exam at various times) say 60 of them attempted the question then the attempt % is 60%

#### Accuracy % in Scaling of Marks

Suppose in the above example out of the 60 students who attempted the question say 30 of them got it correct then accuracy % = (30/60)X100 = 50 %

Now the difficult level of the question or the probability of an average student to get the question correct is

= attempt % X accuracy %

= 60% X 50 %

= 30 %

So in simple term that it is a 30 % Probability that an average student will get the question correct.

Now Lets see How the Scaling of Marks Happen on a Question to Question basis in Scaling of Marks

(Assumption Each Correct Question is 4 Marks , Each Incorrect Question is -1 Marks and Left Question is Zero Marks

Now There are Three Possible Outcomes of any Question

**Student Attempts and Get it correct**

Actual Marks = 4 Marks

Percentile of a student = 100 Percentile

Scaled Marks of the Student = Percentile X Total Marks = 100% X 4 = 4

**Student Attempt it and Get it Wrong**

Actual Marks = -1 Marks

Percentile of the Student = 0 Percentile

Scaled Marks of Student = Percentile of Student X Total Marks = 0% X 4 = 0

- Student Leaves the Questions

Actual Marks of the Student = 0

Percentile of Student = Needs to be Calculated

Scaled Marks of Students = Percentile X Total Mark

Now Lets Try and Calculate the percentile of a student who Leave a question unattempted

Lets take Two Examples

Question 1 (Easy Question)

Attempt % = 90

Accuracy % = 100

Probability of Getting Question Correct = 100 % X 90 % = 90%

Marks Scored by an Average Student = 90% X Total Marks = 90% X 5 = 4.5

(Remember This 4.5 is From -1 as the range of Bell Curve is From -1 to 4 Marks)

So Actual Marks = 4.5-1 =3.5

Question 2 (Difficult Question)

Attempt % = 10 %

Accuracy % = 10 %

Probability of Getting Question Correct = 10 % X 10 % = 1.0%

Marks Scored by an Average Student = 90% X Total Marks = 1% X 5 = 0.05

(Remember This 4.5 is From -1 as the range of Bell Curve is From -1 to 4 Marks)

So Actual Marks = 0.05 – 1 = -0.95

Lets First See Question 1 (Easy Question )

We Know

100 Percentile = 4 Marks

50 Percentile = 3.5 Marks

0 Percentile = -1 Marks

Now Since We have to Calculate the Value of the Percentile for a score Zero which Lies between -1 and 3.5 (Right Sided Curve)

So Percentile would be

= Distance of Zero From Left Side/ (Total Range of Left Side) X 50

= (1 / 4.5 ) X 50 = 11.1111

So the Percentile for a Left Question will be 11.11 Percentile

So Scaled Marked for a Left Question will be = 11.11% X 4 = 0.4444

Now Lets Move to See Question 2 (Tough Question )

We Know

100 Percentile = 4 Marks

50 Percentile = – 0.95Marks

0 Percentile = -1 Marks

Now Since this is a Left Sided Curve

The Distance Between -1 to – 0.95 will Be Considered as 50 Percentile

Now we have to Calculate the Percentile of Distance Between – 0.95 to Zero

= (Distance of 50th Percentile from Zero / Range )X 50 )

= 0.95/(4+0.95) = 0.1919 X 50 = 9.595

Hence total Percentile = 50 + 9.59 = 59.59

Hence Scaled Marks = 59.59% X 4 = 2.3836

Now Let me Show the Calculation for 10 Question Test based on Similar Calculation for Three Type of Question

(Namely Easy , Medium and Tough Question and their Actual Marks and Scaled Marks)

Q No | Attempt % | Accuracy % | Probability Of Getting Question Correct | Question Status | Actual Marks | Marks Scored By 50th Percentile | Percentile Calculation | Scaled Score of Zero Marks | Scaled Marks |

1 | 90 | 100 | 90 | Correct | 4 | 4.5 | 11.1 | 0.44 | 4 |

2 | 90 | 100 | 90 | Left | 0 | 4.5 | 11.1 | 0.44 | 0.44 |

3 | 90 | 100 | 90 | Incorrect | -1 | 4.5 | 11.1 | 0.44 | 0 |

4 | 70 | 70 | 49 | Correct | 4 | 2.45 | 20.4 | 0.82 | 4 |

5 | 70 | 70 | 49 | Left | 0 | 2.45 | 20.4 | 0.82 | 0.82 |

6 | 70 | 70 | 49 | Incorrect | -1 | 2.45 | 20.4 | 0.82 | 0 |

7 | 20 | 20 | 4 | Correct | 4 | 0.2 | 58.3 | 2.33 | 4 |

8 | 20 | 20 | 4 | Left | 0 | 0.2 | 58.3 | 2.33 | 2.3 |

9 | 20 | 20 | 4 | Incorrect | -1 | 0.2 | 58.3 | 2.33 | 0 |

10 | 20 | 100 | 20 | Correct | 4 | 1 | 50.0 | 2.00 | 4 |

Total Marks Actual | 13/40= 32.5% | Total Marks Scaled | 19.5941= 48.98% |

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