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Basics of Normalization with examples

Prashant Prakash's picture
Normalization Resolved
Normalization is one of the favorite topics of interviewee. It does not matter whether you have mentioned DBMS in your resume or not .This question is going to come and the funny part is that all of us know
  • what is normalization?
  • What are the different types of normalization?

So when this question on being asked the interviewer who have already prepared for it start with the history of normalization and end with the geography of normalization but when the next question for which they have not prepared i.e.  apply normalization in real case scenario.

Now here comes the real part of normalization and just because of not proper concepts, people end up confusing themselves. So the idea is to not only to get familiar with normalization but also how to apply it in real time scenario.


What is Normalization?
Database designed based on ER model may have some amount of inconsistency, ambiguity and redundancy. To resolve these issues some amount of refinement is required. This refinement process is called as Normalization. I know all of you are clear with the definition, let’s go with :

  • what is the need of normalization?
  • What are the problems we can face if we proceed without normalization?
  • What are the advantages of normalization?

Asking question to oneself is the best way to get familiar with all the concepts.

The need of Normalization
I am going to show you one simple E-R model database.

Student Details Course Details Result details
1001   Ram               11/09/1986 M4       Basic Maths                       7 11/11/2004       89           A
1002   Shyam           12/08/1987 M4       Basic Maths                       7 11/11/2004       78           B
1001   Ram               23/06/1987 H6                                                    4 11/11/2004       87           A
1003   Sita                16/07/1985 C3        Basic Chemistry                 11 11/11/2004       90           A
1004   Gita               24/09/1988 B3                                                     8 11/11/2004       78           B
1002   Shyam           23/06/1988 P3        Basic Physics                     13      11/11/2004       67           C
1005   Sunita           14/09/1987 P3        Basic Physics                      13 11/11/2004       78           B
1003   Sita                23/10/1987 B4                                                      5 11/11/2004       67           C
1005   Sunita           13/03/1990 H6                                                     4 11/11/2004       56           D
1004   Gita               21/08/1987 M4      Basic Maths                         7 11/11/2004       78           B
 
In first look the above table is looking so arranged and well in format but if we try to find out what exactly this table is saying to us , we can easily figure out the various anomalies in this table . Ok let me help you guys in finding out the same.
  1. Insert Anomaly: We cannot insert prospective course which does not have any registered student or we cannot insert student details that is yet to register for any course.
  2. Update Anomaly: if we want to update the course M4’s name we need to do this operation three times. Similarly we may have to update student 1003’s name twice if it changes.
  3. Delete Anomaly: if we want to delete a course M4 , in addition to M4 occurs details , other critical details of student also will be deleted. This kind of deletion is harmful to business. Moreover, M4 appears thrice in above table and needs to be deleted thrice.
  4. Duplicate Data: Course M4’s data is stored thrice and student 1002’s data stored twice .This redundancy will increase as the number of course offerings increases.
Process of normalization:
Before getting to know the normalization techniques in detail, let us define a few building blocks which are used to define normal form.
  1. Determinant : Attribute X can be defined as determinant if it uniquely defines the value Y in a given relationship or entity .To qualify as determinant attribute need NOT be a key attribute .Usually dependency of attribute is represented as X->Y ,which means attribute X decides attribute Y.
Example: In RESULT relation, Marks attribute may decide the grade attribute .This is represented as Marks->grade and read as Marks decides Grade.
Marks -> Grade
In the result relation, Marks attribute is not a key attribute .Hence it can be concluded that key attributes are determinants but not all the determinants are key attributes.
 
  1. Functional Dependency: Yes functional dependency has definition but let’s not care about that. Let’s try to understand the concept by example. Consider the following relation :
REPORT(Student#,Course#,CourseName,IName,Room#,Marks,Grade)
Where:
  • Student#-Student Number
  • Course#-Course Number
  • CourseName -CourseName
  • IName- Name of the instructor who delivered the course
  • Room#-Room number which is assigned to respective instructor
  • Marks- Scored in Course Course# by student Student #
  • Grade –Obtained by student Student# in course Course #
  • Student#,Course#  together (called composite attribute) defines EXACTLY ONE value of marks .This can be symbolically represented as
                                Student#Course# Marks
This type of dependency is called functional dependency. In above example Marks is functionally dependent on Student#Course#.
Other Functional dependencies in above examples are:
  • Course# -> CourseName
  • Course#-> IName(Assuming one course is taught by one and only one instructor )
  • IName -> Room# (Assuming each instructor has his /her own and non shared room)
  • Marks ->Grade
Formally we can define functional dependency as: In a given relation R, X and Y are attributes. Attribute Y is functional dependent on attribute X if each value of X determines exactly one value of Y. This is represented as :
                X->Y
However X may be composite in nature.
 
  1. Full functional dependency: In above example Marks is fully functional dependent on student#Course#  and not on the sub set of Student#Course# .This means marks cannot be determined either by student # or Course# alone .It can be determined by using Student# and Course# together. Hence Marks is fully functional dependent on student#course#.
CourseName is not fully functionally dependent on student#course# because one of the subset course# determines the course name and Student# does not having role in deciding Course name .Hence CourseName is not fully functional dependent on student #Course#.
               
Student#
                  Marks
Course#
Formal Definition of full functional dependency : In a given relation R ,X and Y are attributes. Y is fully functionally dependent on attribute X only if it is not functionally dependent on sub-set of X.However X may be composite in nature.
 
  1. Partial Dependency: In the above relationship CourseName,IName,Room# are partially dependent on composite attribute Student#Course# because Course# alone can defines the coursename, IName,Room#.
Room#
IName
CourseName
Course#
Student#
Formal Definition of Partial dependency: In a given relation R, X and Y are attributes .Attribute Y is partially dependent on the attribute X only if it is dependent on subset attribute X .However X may be composite in nature.
 
  1. Transitive Dependency:  In above example , Room# depends on IName and in turn depends on Course# .Here Room# transitively depends on Course#.
IName
Room#
Course#              
Similarly Grade depends on Marks,in turn Marks depends on Student#Course#  hence Grade
Fully transitively depends on Student#Course#.
 
  1. Key attributes : In a given relationship R ,if the attribute X uniquely defines all other attributes ,then the attribute X is a key attribute which is nothing but the candidate key.
Ex: Student#Course# together is a composite key attribute which determines all attributes in relationship REPORT(student#,Course#,CourseName,IName,Room#,Marks,Grade)uniquely.Hence Student# and Course# are key attributes.
 
Types of Normal Forms
  1. First Normal Form(1NF)
A relation R is said to be in first normal form (1NF) if and only if all the attributes of the relation R are atomic in nature 
Student Details Course Details Result details
1001   Ram               11/09/1986 M4       Basic Maths                       7 11/11/2004       89           A
1002   Shyam           12/08/1987 M4       Basic Maths                       7 11/11/2004       78           B
1001   Ram               23/06/1987 H6                                                    4 11/11/2004       87           A
1003   Sita                16/07/1985 C3        Basic Chemistry                 11 11/11/2004       90           A
1004   Gita               24/09/1988 B3                                                     8 11/11/2004       78           B
1002   Shyam           23/06/1988 P3        Basic Physics                     13      11/11/2004       67           C
1005   Sunita           14/09/1987 P3        Basic Physics                      13 11/11/2004       78           B
1003   Sita                23/10/1987 B4                                                      5 11/11/2004       67           C
1005   Sunita           13/03/1990 H6                                                     4 11/11/2004       56           D
1004   Gita               21/08/1987 M4      Basic Maths                         7 11/11/2004       78           B
 
Table shown above Student Details ,Course Details and Result Details can be further divided. Student Details attribute is divided into Student#(Student Number) , Student Name and date of birth. Course Details is divided into Course# ,Course Name,Prerequisites and duration. Similarly  Results attribute is divided into DateOfexam,Marks and Grade.
 
  1. Second Normal Form (2NF)
A relation is said to be in Second Normal Form if and only If :
  • It is in the first normal form ,and
  • No partial dependency exists between non-key attributes and key attributes.
           
Let us re-visit 1NF table structure.
  • Student# is key attribute for Student ,
  • Course# is key attribute for Course
  • Student#Course#  together form the composite key attributes for result relationship.
  • Other attributes are non-key attributes.
To make this table 2NF compliant, we have to remove all the partial dependencies.
  • StudentName and DateOfBirth depends only on student#.
  • CourseName,PreRequisite and DurationInDays depends only on Course#
  • DateOfExam depends only on Course#.
To remove this partial dependency we need to split Student_Course_Result table into four separate tables ,STUDENT ,COURSE,RESULT and EXAM_DATE tables as shown in figure.

STUDENT TABLE
Student # Student Name DateofBirth
1001 Ram Some value
1002 Shyam Some value
1003 Sita Some value
1004 Geeta Some value
1005 Sunita Some value
 
COURSE TABLE
Course# CourseName Duration of days
C3 Bio Chemistry 3
B3 Botany 8
P3 Nuclear Physics 1
M4 Applied Mathematics 4
H6 American History 5
B4 Zoology 9

RESULT TABLE
Student# Course# Marks Grade
1001 M4 89 A
1002 M4 78 B
1001 H6 87 A
1003 C3 90 A
1004 B3 78 B
1002 P3 67 C
1005 P3 78 B
1003 B4 67 C
1005 H6 56 D
1004 M4 78 B
 
EXAM DATE Table
Course# DateOfExam
M4 Some value
H6 Some value
C3 Some value
B3 Some value
P3 Some value
B4 Some value
 
  • In the first table (STUDENT) ,the key attribute is Student# and all other non-key attributes, StudentName and DateOfBirth are fully functionally dependant on the key attribute.
  • In the Second Table (COURSE) , Course# is the key attribute and all the non-key attributes, CourseName, DurationInDays are fully functional dependant on the key attribute.
  • In third table (RESULT) Student#Course# together are key attributes and all other non key attributes, Marks  and Grade are fully functional dependant on the key attributes.
  • In the fourth Table (EXAM DATE) Course# is the key attribute and the non key attribute ,DateOfExam is fully functionally dependant on the key attribute.
At first look it appears like all our anomalies are taken away ! Now we are storing Student 1003 and M4 record only once. We can insert prospective students and courses at our will. We will update only once if we need to change any data in STUDENT,COURSE tables. We can get rid of any course or student details by deleting just one row.

Let us analyze the RESULT Table
Student# Course# Marks Grade
1001 M4 89 A
1002 M4 78 B
1001 H6 87 A
1003 C3 90 A
1004 B3 78 B
1002 P3 67 C
1005 P3 78 B
1003 B4 67 C
1005 H6 56 D
1004 M4 78 B
 
We already concluded that :
  • All attributes are atomic in nature
  • No partial dependency exists between the key attributes and non-key attributes
  • RESULT table is in 2NF
 
Assume, at present, as per the university evaluation policy,
  • Students who score more than or equal to 80 marks are awarded with “A” grade
  • Students who score more than or equal to 70 marks up till 79 are awarded with “B” grade
  • Students who score more than or equal to 60 marks up till 69 are awarded with “C” grade
  • Students who score more than or equal to 50 marks up till 59 are awarded with “D” grade
 
The University management which is committed to improve the quality of education ,wants to change the existing grading system to a new grading system .In the present RESULT table structure ,
  • We don’t have an option to introduce new grades like A+ ,B- and E
  • We need to do multiple updates on the existing record to bring them to new grading definition
  • We will not be able to take away “D” grade if we want to.
  • 2NF does not take care of all the anomalies and inconsistencies.
 
  1. Third Normal Form (3NF)
A relation R is said to be in 3NF if and only if
  • It is in 2NF
  • No transitive dependency exists between non-key attributes and key attributes.
In the above RESULT table Student# and Course# are the key attributes. All other attributes, except grade are non-partially , non – transitively dependant on key attributes. The grade attribute is dependant on “Marks “ and in turn “Marks” is dependent on Student#Course#. To bring the table in 3NF we need to take off this transitive dependency.
 
Student# Course# Marks
1001 M4 89
1002 M4 78
1001 H6 87
1003 C3 90
1004 B3 78
1002 P3 67
1005 P3 78
1003 B4 67
1005 H6 56
1004 M4 78
 
UpperBound LowerBound Grade
100 95 A+
94 90 A
89 85 B+
84 80 B
79 75 B-
74 70 C
69 65 C-
 
After Normalizing tables to 3NF , we got rid of all the anomalies and inconsistencies. Now we can add new grade systems, update the existing one and delete the unwanted ones.
Hence the Third Normal form is the most optimal normal form and 99% of the databases which require efficiency in
  • INSERT
  • UPDATE
  • DELETE
Operations are designed in this normal form.
 
Hope this article will be useful to engineering students and to interviewer too!

You can download the pdf format of this article from here
You can view this article at our slideshare page too:

 
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sanjeev's picture
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Joined: 21 Feb 2011
Very nice explanation on Normalization
Well Done Prashant.
Answer to this question was much awaited.
You have explained all the terms and all basic forms of normalization with a very simple example.

I liked it and you have answered our one of the interview questions list on DBMS.
Here is the link for all DBMS questions: http://www.aliencoders.com/content/interview-questions-computer-science-...

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Anonymous (not verified)
nice 1
must go through it..
pinklyrics (not verified)
www.aliencoders.com is slow
www.aliencoders.com loads very slow, you should optimize it 
Savan Patel (not verified)
Awesome.
This is what I wanted. I was never able to understand the topic in the class. This site helped me to get clear wit all the concepts.It would be better if this also explains about BCNF , 4th and 5th normal form as well. :-):-)
Anonymous (not verified)
nice one thanks...
nice one thanks...
Anonymous (not verified)
Great
Great sample. Thank you very much!
Anand (not verified)
Thank u Prashant. Its simple
Thank u Prashant. Its simple and clear.
Vivek Mapare (not verified)
Normalization Good Article


It it very nice article which solved my all doubts about the concept of normalization.

Thanks
Vivek Mapare
Software Developer
Aloha Technology Pvt Ltd.

SRUTHI (not verified)
Nice article
Nice article
Sonal Goyal (not verified)
It is very helpful in
It is very helpful in learning normalization. Please explain  BCNF also. Thanks. :)

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