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# Venn Diagram

Go to solution Solved by Sourabh Nandi,

Venn Diagram represents how groups or sets of data relate to each other. It uses circles to represent the groups. Intersecting circles represent some common features among the groups. Sometimes all the groups are enclosed in a rectangle (the universal group).

An application-oriented question on the topic along with responses can be seen below. The best answer was provided by Sourabh Nandi on 31st Jul 2020

Applause for all the respondents - Ram Kumar Chaudhary, Sourabh Nandi

## Question

Q 283. Venn Diagrams represent how groups relate to each other. How can Venn Diagrams be used in problem solving? Explain with example(s)

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• Solution

What is a Venn diagram?

John Venn who coined the Venn diagram in 1880 was an English mathematician, logician and philosopher. He also called them Euler diagrams after Leonhard Euler, who checked them out a century before. This is an extraordinarily flexible technique of combining circles useful for identify the contrast between overlapping areas of uniqueness. This representation of how groups relate to one another are generally called “sets”.

There must be minimum two number of circles, and also the probability of maximum for many uses is 3. However, there can be more shapes in a diagram based on the number of sets and such a diagram can use unique shapes as per the below figures.

Once the circles are interlocked, they reveal discrete areas (in which there’s no overlap). These again compared with the qualities of the overlap areas. Where there are three circles, the central area will show multiple overlapping characteristics. The volume of areas revealed should ideally be kept approximately proportional to their percentage of overlap, in order that the extent of the basic is visually representative.

When to use a Venn diagram

We often see Venn diagrams in mathematical contexts, but businesses and professionals also use these forms. In each case, the person creating the illustration wants to resolve a controversy, make a crucial decision, predict probabilities or visualize or understand how multiple sets or objects relate to at least one another.

Instances when a Venn diagram might be useful in Business

Market analysis:  A Business Analysis Practitioner might use a Venn’s diagram for basic market research. While using two or more sets of data members within the meeting observe overlapping areas, as those areas contain the business’ target market.

Competitor Analysis: A firm might use Venn diagrams to match themselves for their products to their competition. Most times, the business of using the Venn’s diagram may only use two sets of data to work out how they differ from the competition and find any similarities. This helps the business discover what advantages they have already got and specialize in areas where they will make improvements.

Product Comparison:  Alternatively, a business analyst may create an example with overlapping shapes to weigh the advantages of two or more work ideas. Within the same way that the business analyzes the market, a business analyst will weigh any differences and similarities two or more ideas share to work out which features of a product are the foremost desirable, as shown within the overlapping areas.

Decision-Making:  The same principles for analyzing two or more product ideas apply to a business’ general decision-making process.

A Venn diagram provides the following advantages:

• It allows an analyst to visualize concepts and relationships between two or more data.
• It defines complex information into terms that an analyst can understand and represent easily.
• It helps an analyst to better keep information.

Venn diagram symbols

• “∪ ” Union of two sets. An entire Venn diagram represents the union of two sets.
• “ ∩ “ Intersection of two sets. This type of intersection shows what items it shares between categories.
• “ Ac “ Complement of a Set. The compliment is that they don’t represent whatever in an exceedingly set.

An classic example of Venn Diagrams;

In a survey of the fast-food preferences of three people. We assign these three people as A, B, and C, showing which restaurants they enjoy. A three-circle diagram mostly covers every possibility that they’ll choose a restaurant by one, two, three or no respondents.

Scores for Restaurant Survey Results:

 Restaurant A B C McDonald's 1 0 1 Wendy's 1 1 0 Burger King 0 0 0 In-N-Out 0 1 1 Taco Bell 1 0 1 KFC 0 0 0 A&W 0 0 0 Chick-fil-A 1 1 1

While creating the Venn diagram representing the results, we observed that in A∩B, we’ve Wendy’s because respondent A and respondent B both chose it. Few fast-food restaurants like Burger King, KFC & A&W remain outside the diagram but exist within the universe. Since all the three people have chosen Chick-fil-A, the intersection of all three represents A∩B∩C.  So the final Venn diagram will represent in the below figure.

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Venn diagram is a visual method ( usually used in set theory) to enable building perspective about a problem or causes. This enables developing appropriate solution for the problem or causes identified by enabling breaking down of whole situation into smaller disparate components. Example hypothetical scenarios

1. Fatal error in transaction processing : Analyst processing transaction is new, type of transaction picked is complex , team leader is on leave; when these three situations come together, there is a high probability of a fatal error happening. At the intersection of these three circles is the red zone, hence such a situation should be mitigated. Venn diagram provides a simplified way of communication such combination of situations to operations staff for watch out.

2. Not meeting our contractual productivity improvement commitment for a client. When probed further basis experience following components surfaced, a) Delivery not meeting basic SLA's (hence there focus was on improving SLA performance  b) Process Excellence not having a plan ( used to engage with delivery on adhoc basis) and c) Client team changing priorities frequently. This resulted in a situation of multiple initiatives none crossing the finishing line

3. Looking at which subset is causing maximum issue, example call quality not meeting client expectation. Similar to pareto looking at sub parts of call quality form where team is not able to meet standards. It appeared form had 5 parts and team was meeting/exceeding expectation on 4 parts and significantly missing on one part (Customer experience) - dead air & hold time. In order to resolve calls accurately team members were validating with SME's /Team leads, hence putting customers on hold frequently resulting in significant dip in customer experience.

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Sourabh Nandi has provided the best answer to this question by providing business applications of Venn Diagrams along with an example. Congratulations!

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