Illustrates the calculation of difficulty index

1. Pilot
Study
Pilot study is a small scale advance administering
of the question paper to students to stabilize the
questions. Here we have to administer the
questions to 100 students and collect the marks.
From the obtained marks we have to go for
statistical calculation. Since, it is lock down period
now, I will be giving the marks for 10 students. (If
number of students is more, statistical predictions
will become accurate)

2. Difficulty
Index -
Concept
✓ As the name indicates, it says how
easy or difficult a question is.

4. Difficulty
Index -
Formula
No. of Students correctly
answered a question
DI = ---------------------------------
Total No. of Students

5. Difficulty
Index -
Concept
✓ Difficulty Index (DI) will have to be
calculated for each question
✓ For a question, It is the ratio of the
students who answered correctly to the
total number of students
✓ For example, let us take the 1st question. If
that question is answered correctly by 4
out of 10 students then, the index of
difficulty is
=4/10 = 0.4

6. DI -
Calculation
✓ Calculate DI for the 2nd question. It is
correctly answered by 9 students out of 10.
✓ DI=9/10= 0.9
✓ Compare DI of question 1 with question 2.
.

7. DI -
Calculation
✓ DI for Q1 = 0.4, Correctly answered 4/10
DI for Q2 = 0.9, Correctly answered 9/10
This means that if DI is low then, question
is hard and high then, question is
easy.
✓ Out of Q1 and Q2 which is easy?
Q2 is easier than Q1
.

8. DI -
Relationship
✓ What is the proportionality between DI
and difficultness of a question?
✓ Inversely proportional.
✓ If DI is high then, it is easy question
and low then, it is hard question
.

9. DI -
Range
✓ What is the range of DI.
✓ Think of two cases, one in which everybody
answers a question and in other nobody
answers a question

10. DI -
Range
✓ It is 0 to 1.
✓ If DI=1, everybody correctly answered the
question.
✓ If DI=0, Nobody correctly answered the
question.

11. DI
✓ Likewise you can calculate DI for all questions.
✓ Calculating DI for first 20 questions is easy and
further we face difficulty. What is the problem
in calculating DI from Q21?

12. DI –
Subjective
and
Objective
Questions
✓ From Q1 to Q20, it is objective questions. After
that it is subjective questions. For objective
questions if the answer is correct, the mark is 1
and if it is wrong, the mark is 0. This is not the
case for Q21 to Q29. How to calculate DI for
that?

13. DI for
subjective
question
✓ This can be handled easily like this. If the mark
is more than 70% for a question then it is
considered as 1 otherwise 0.
✓ For example, let us take Q21. The maximum
marks is 3 and 70% of 3 is 2.1≈2. Hence if a
student gets 2 or more marks, it is taken as 1
and if he/she gets less than 2 marks it is taken
and 0. Now it becomes easy to calculate DI
.

14. DI for
subjective
question
✓ Let us go for calculation of DI for subjective
question. For Q21, 8 students got 2 and above
out of 10 students. Calculate DI.
✓ DI = 8/10 = 0.8

15. DI for
subjective
question
✓ For Q22, 2 students got 2 and above out of 10
students. Calculate DI.
✓ DI = 2/10 = 0.2
✓ For Q23, 2 students got less than 2 out of 10
students. Calculate DI.
✓ DI = 8/10 = 0.8
(if 2 students got less than 2 means 8
students would have got 2 and above)

16. DI for 5
Mark
Question
✓ What is 70% of 5? It is 3.5.
✓ 3.5 is borderline for 1 or 0. Hence if a student
gets 3.5 or more marks, it is taken as 1 and if
he/she gets less than 3.5 marks it is taken and 0
✓ For Q26, 9 students got 3.5 and above out of 10
students. Calculate DI.
✓ DI = 9/10 = 0.9

17. Assessme
nt
✓ Now you know, how to calculate DI for objective
and subjective questions.
✓ After calculation, you will come to know that
which question is easy and which is difficult. If
DI is low then, it is difficult question and high
then, it is question.
✓ What do you think to be done with the DI
value?

18. Assessme
nt
✓ Highly difficulty and very easy question are to
be avoided. Since for highly difficult question,
nobody will attend and very easy question,
everybody will attend and get full marks like the
question, which is the capital of India?

19. Judgment
S.No. DI Level Result
1 0-0.3 Difficult Rejected
2 0.31-0.79 Moderate Selected
3 >0.80 Easy Rejected

20. Implications
✓ Based the table in previous slide, one has to
select or reject the question.
✓ If all questions are selected no problem. If
some questions are rejected what is to be
done?

21. Implications
✓ Again write the question, go for pilot study,
calculate new DI and based on it select or
reject the question.

22. For
Understanding
✓ Very Easy and highly difficult questions are to
be avoided. Only moderate questions need
to be kept in the question paper.

23. Model Data
✓ Model data is attached in the following slide.
It gives DI for all the questions. Data is
hypothetically given for learning purpose.
✓ Data Courtesy: Mr. Sridath

24. Q.NO. S1 S2 S3 S4 S5 S6 S7 S8 S9 S10
No. of Stu.
Who Ans.
Corr.
Tot. No.
of Stu.
DI Level Decision
1 1 1 1 1 1 1 1 1 1 1 10 10 1 EASY REJ
2 1 1 1 1 1 1 0 1 0 1 8 10 0.8 MOD REJ
3 0 1 1 1 1 0 0 1 0 1 6 10 0.6 MOD SEL
4 1 0 1 1 0 0 1 1 1 1 7 10 0.7 MOD SEL
5 1 1 1 1 1 1 1 1 0 0 8 10 0.8 MOD SEL
6 1 1 1 1 1 1 1 1 1 1 10 10 1 EASY REJ
7 1 1 1 1 1 1 1 1 1 1 10 10 1 EASY REJ
8 0 0 1 0 0 1 0 1 1 0 4 10 0.4 MOD SEL
9 1 1 0 0 1 0 1 0 1 1 6 10 0.6 MOD SEL
10 0 1 0 1 1 1 1 0 1 1 7 10 0.7 MOD SEL
11 1 1 1 1 1 0 0 1 0 1 7 10 0.7 MOD SEL
12 1 1 1 0 0 1 1 1 1 0 7 10 0.7 MOD SEL
13 1 1 0 1 1 1 1 0 1 1 8 10 0.8 MOD SEL
14 1 1 1 1 1 1 1 1 1 1 10 10 1 EASY REJ
15 0 0 1 0 1 0 0 1 1 1 5 10 0.5 MOD SEL
16 1 1 1 1 1 1 1 1 0 1 9 10 0.9 EASY REJ
17 1 0 0 1 1 1 0 1 0 1 6 10 0.6 MOD SEL
18 1 1 1 1 1 1 1 1 0 0 8 10 0.8 MOD SEL
19 1 1 1 0 0 1 1 0 1 1 7 10 0.7 MOD SEL
20 0 1 1 1 1 0 1 0 1 1 7 10 0.7 MOD SEL
21 2 2 2.5 2.5 2 2 2 2.5 2 2 10 10 1 EASY REJ
22 1.5 1.5 2 1.5 1.5 2 2.5 2 1.5 2.5 5 10 0.5 MOD SEL
23 3 3 3 3 3 3 3 3 3 3 10 10 1 EASY REJ
24 2.5 2 2 2.5 2 1.5 2 1.5 2 2 8 10 0.8 MOD SEL
25 3 2 2.5 2 1.5 2 2.5 2.5 2 2 9 10 0.9 EASY REJ
26 4 3 3.5 3 2.5 2 3.5 4 4.5 4 6 10 0.6 MOD SEL
27 3 3 4 3 5 3 5 3 3 4 5 10 0.5 MOD SEL
28 4 4 4 3 4 3 4 4 4 4 8 10 0.8 MOD SEL
29 0 0 0 0 0 0 0 0 0 0 0 10 0 DIFF REJ

25. Assignment
✓ Based on the previous slide, have
hypothetical for all questions for ten
students. Calculate DI and take decision
whether to accept or reject the questions.

26. References
• Mathew, T.K., and Mollykutty, T.M. (2011). Science Education -Theoretical bases
of teaching and pedagogic analysis - Physical Science and Natural Science.
Kerala: Rainbow Book Publishers
• NCERT. (2013). Teaching of science. Delhi: Author
• Radha Mohan. (2007). Teaching of physical science. (3rd ed.). Delhi: PHI Learning
• Rathinasabapathy, P. (2001). கல்வியில் தேர்வு [Examination in Education].
(2nd ed.). Chennai: Shantha Publishers.
• Srinivasan, P. (2011). அறிவியல் கற்பிே்ேல் [Teaching of science].
Thanjavur: DDE, Tamil Univeristy
• Images from google