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Welcome to the guide on Venn Diagrams

Please note this topic is a big differentiator in getting a high score

There are no Prequisites for this lesson.

A venn diagram is a visual way of representing relationships between a collection of data points. Be sure to visit the click here for some basic information and terminology.

Reading check:

  1. What does union mean? How is it represented?

  2. What does intersection mean? How is it represented?

  3. What does complement mean? How is it represented?

  4. What is a universal set? What is an empty set?


If you find yourself confused about any of these terms, be sure to go back to the site and review them! They will be very important moving forward.  

The data represented in the venn diagrams you saw on the website were all qualitative data, meaning the data was non-numeric and unstructured. However, we often see venn diagrams representing quantitative data as well. Quantitative data contains information about quantities and is numeric.

Click the following links for more information and to see how venn diagrams are used for quantitative data:

  • Introduction (The first site to visit giving a basic introduction)  

  • 3 part Venn Diagrams reading (this is on three-way Venn diagrams, which can be a little tricky!)

  • Video (here is a Youtube video for more visual learners!))  

  • Guided practice (If you’re still having trouble understanding, click this link to see a walkthrough of a problem)

Pro tip: Work from the center and move outwards! 

Practice and check your understanding with the practice sheets available here:

  • Practice worksheet (Click on the following link for practice problems. The answers are after all of the problems. It is recommended that you do ALL of the problems from this site.) 

Now check if you are battle-ready by answering the following questions:

1. Sixty high school seniors were polled to see if they were taking history and calculus. A total of 29 students said they were taking calculus, and a total of 50 students said they were taking history. What is the minimum number of students who take both history and calculus? Assume every student takes at least one of these courses. (Hint: draw out the venn diagram!)​​

2. Forty students play soccer and/or basketball after school. Twenty-four students play soccer and twenty-nine play basketball. How many students play both soccer and basketball? Assume every student takes at least one of these courses.

3. In a class of senior high-school students, 13 have pet cats, 12 have pet dogs, 5 have both cats and dogs, and 8 have neither cats nor dogs. How many total students are in the class?

4. Fifty 6th graders were asked what their favorite school subjects were.  Three students like math, science and English.  Five students liked math and science.  Seven students liked math and English.  Eight people liked science and English.  Twenty students liked science.  Twenty-eight students liked English.  Fourteen students liked math.  How many students didn’t like any of these classes?

5. Determine if each observation is qualitative or quantitative:

6. In a class, there are 15 students who like chocolate. 13 students like vanilla. 10 students like neither. If there are 35 people in the class, how many students like chocolate and vanilla?

7. A given company has 1500 employees. Of those employees, 800 are computer science majors. 25% of those computer science majors are also mathematics majors. That group of computer science/math dual majors makes up one third of the total mathematics majors. How many employees have majors other than computer science and mathematics?

8. In a school, 70 students are taking classes. 35 of them will be taking Accounting and 20 of them will be taking Economics. 7 of them are taking both of these classes. How many of the students are not in either class?


To see the answers, click here 

Congrats on reaching the end of this lesson. If you did not understand any concept be sure to go back through and review, so that you can be fully prepared. We learn the most from our mistakes so don’t be disheartened by them. When you feel that you are ready, go ahead and take a little break. Then come back and move onto another section!

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