Venn diagrams are visual classifications that show relationships between certain sets of things. They’re probably the easiest diagram to understand, because they’re so simple! They’re just made up of overlapping circular shapes, populated with different variables. The area that these variables are located say something about both the variable itself, and its relation to the other variables represented in the diagram. It’s easy to understand once you start looking at some charts, plus it’s a handy way of categorizing and comparing information.

In this guide, we’ll show you some examples of venn diagrams, and give you some venn diagram problems so you can work on creating your own. Once you understand the basic venn diagram rules and applications, you can start creating some pretty complex ones to classify your sets of data.

Venn diagrams are commonly used in the field of statistics. Check out this course for an introduction to statistics.

## What is a Venn Diagram?

So the best way to understand what a venn diagram does is to just look at one. But, we can’t have a venn diagram without data to categorize, so let’s think up a quick problem right here.

Say you have a list of animals: dog, cat, dolphin, beaver, tuna, octopus, polar bear, horse, and otter. You want to categorize them into categories: things with fur, and water animals, which would be animals that live in or around bodies of water. The thing is, many of the animals in our list fit into both categories – so how would we represent that in a diagram, without needing to create multiple visualizations?

As you can see, in the venn diagram above, we have dolphin, tuna, and octopus in the left circle, which classifies water animals, and we have dog, cat, and horse in the right circle, which classifies things with fur. In the overlap between the two circles, we have beaver, polar bear, and otter, because the three of these animals both live in the water and have fur. With venn diagrams, we’re able to easily represent the overlap between two categories of data and the information within each set, without the need to create multiple diagrams. It’s efficient and easy to understand. Check out this introductory statistics course for more ways to analyze sets of data.

If you want to create your own venn diagrams like the one above, check out this venn diagram generator on ReadWriteThing.org. This is where the diagrams in this guide were created in, and it’s a good way for you to efficiently create your own to solve the venn diagram problems below. If you don’t want to use this source, you can also use a program like Microsoft Visio. Check out this introduction to Micrisoft Visio 2013 to get started.

## Venn Diagram Problems

Now that we know what venn diagrams are and how they work, let’s examine more sets of data and figure out how to categorize each. For more tips and techniques for analyzing sets of data, and calculating other things like probability, check out this statistics workshop.

Categorizing Classes

Here’s an easy one. Say you start with a set of data that contains the following:

• Susie (English major)
• Jose (Computer Science major)
• Tommy (English major)
• Christine (English and Computer Science double major)
• Terrell (Computer Science major)
• Maria (English major)
• Lisa (Computer Science major)
• Bob (English major)
• Jorge (English and Computer Science double major)

You want to categorize these students depending on their major – English, or Computer Science. What would the venn diagram for this venn diagram problem look like? If you want to get into some more advanced stats, check out this descriptive statistics course.

Friends List

Let’s say a super nerdy kid wanted to create a venn diagram to keep track of her friends and acquaintances at her high school. She has two primary groups of friends: people she knows from her chess club, and people she knows from volunteering after school at the homeless shelter. She knows a couple of these people from both.

• Maria (Chess club)
• John (Chess club)
• Raleigh (Volunteer work)
• Julia (Both)
• Candace (Volunteer work)
• Ralph (Chess club)
• Robert (Both)
• Brandy (Chess club)
• Nancy (Both)
• Ryan (Volunteer)

How would you categorize this set of data? Check out this course on inferential statistics for more advanced concepts.

## Identifying Relationships

Things get tricky when you don’t have the categorizations laid out for you, like they were in previous examples. It’s one thing to sort through data and assign it a place on a clearly labeled diagram, but what if you just have a set of data and need to figure out the categories by ourselves? This means we’re the one in charge of coming up with the classifications, of identifying relationships between items in a set of data, and of organizing those on a comprehensible chart. Think critically about the set of data below, and figure out what each item in the list has in common and what they don’t, and create a venn diagram based on your findings.

• Airplane
• Seagull
• Helicopter
• Iguana
• Zeppelin
• Platypus
• Hot-air balloon
• Marlin
• Goldfish
• Pelican
• Python
• Drone
• Salmon
• Pigeon
• Bee
• Duck
• Jet

Critical thinking is a vital skill when analyzing data. Check out this course on developing your critical thinking skills easily or this critical thinker academy course. You can also consult this guide on nine critical thinking exercises you should be practicing.

Below you’ll find the answers to each of the three venn diagram problems above.

Categorizing Classes

Friends List

Identifying Relationships

This one was pretty tricky! The huge list of data that included a combination of human made objects and animals could be grouped into three categories: things that fly, things that lay eggs, and things that do both! Check out the venn diagram below for an example of how yours should look.

Want to become a data scientist? Check out this guide to learn how. If you want to learn how to use venn diagrams for more advanced data analysis, check out this guide on partial correlation.

Page Last Updated: February 2020