Statistics – Venn Diagram

enn diagram is a way to visually represents relationship between groups of entities or objects. Venn diagrams are comprised of circles where each circle represents a whole set. Venn diagram can have unlimited circles but generally two or three circles are preferred otherwise the diagram becomes too complex.

Steps to draw a Venn Diagram

Consider the following sets of people:

  1. Cricket Players – C={Ram,Shyam,Mohan,Rohan,Ramesh,Suresh}C={Ram,Shyam,Mohan,Rohan,Ramesh,Suresh}
  2. Hockey Players – H={Ramesh,Naresh,Mahesh,Leela,Sunita}H={Ramesh,Naresh,Mahesh,Leela,Sunita}

Step 1: Draw a rectangle and label it as players.

Step 2: Draw two circles and label them as Cricket and Hockey. Make sure that circles are overlapping each other.

Step 3: Write Names inside the circle as relevant. Common name(s) should fall within common region.

C & H Venn Diagram

Union

Union () represents a set where items are present in all categories but are not repeated.

Example

Problem Statement:

Draw a Venn diagram of CHC∪H.

Solution:

Step 1: Determine players who are either playing cricket or hockey. Draw them as following:

CH={Ram,Shyam,Mohan,Rohan,Ramesh,Suresh,Naresh,Mahesh,Leela,Sunita}C∪H={Ram,Shyam,Mohan,Rohan,Ramesh,Suresh,Naresh,Mahesh,Leela,Sunita}.

C Union H Venn Diagram

Intersection

Intersection () represents a set where items are present in both categories.

Example

Problem Statement:

Draw a Venn diagram of CHC∩H.

Solution:

Step 1: Determine players who are playing cricket and hockey both. Draw them as following:

CH={Ramesh}C∩H={Ramesh}.

C Intersection H Venn Diagram

Difference

Difference () represents a set where items are present only in one category and not in other one.

Example

Problem Statement:

Draw a Venn diagram of CHC−H.

Solution:

Step 1: Determine players who are playing cricket only. Draw them as following:

CH={Ram,Shyam,Mohan,Rohan,Suresh}C−H={Ram,Shyam,Mohan,Rohan,Suresh}.

C - H Venn Diagram