Statistics How To

Draw a Venn Diagram in Statistics: Easy Steps

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Venn diagrams are a way to visualize relationships between groups of objects. They are often confused with Euler diagrams. While both have circles, Venn diagrams show the whole of a set while Euler diagrams can show parts of a set. Venn diagrams can have unlimited circles, but more than three becomes extremely complicated so you’ll usually see just two or three circles in a Venn diagram drawing.

Draw a Basic Venn Diagram.


Sample question: Draw a Venn diagram to show categories of “indoor” and “outdoor” for the following pets:
Cat, Goat, Rabbit, Tortoise, Hamster, Fish, Horse, Parrot.

Step 1: Categorize your items (in this case, pets):
Indoor pets: Hamster, Fish, Parrot.
Outdoor pets: Goat, Tortoise, Horse.
Both categories (indoor and outdoor): Cat, Rabbit.

Step 2: Draw a rectangle and label it. For this sample question, label the rectangle “Pets.”

Step 3: Draw two or three circles according to how many categories you have. There are two categories in the sample question: “indoor pets” and “outdoor pets”, so draw two circles. Make sure the circles overlap.
draw a venn diagram 1

Step 4: Write your items in the relevant circle. If items fit both categories, write those where the circles overlap (the “intersection”).
venn diagram 2.

Tip: If you had a pet that doesn’t fit a category (a virtual pet, for example, might not fit either category), write it within the rectangle but outside the circles.
venn diagram 3
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Draw a Venn Diagram of A ∩ B: Overview


An Intersection (∩) in Venn diagrams is when items appear in both categories presented (not one or the other). The intersection is written as A ∪ B where A is one category and B is a second category. The ∪ means “intersection,” which in the example above were the pets that were both indoor and outdoor : cats and rabbits. It’s written as:
Indoor ∩ Outdoor = {cats,rabbits}.
Which way does the ∪ go? An easy way to remember is that the union is the ∪ (so by default, the intersection is the other one!).

Draw a Venn Diagram of A ∩ B: Steps

Sample question: Draw a Venn Diagram of A ∩ B (Intersection) of “black things” and “white things”:
Coal, Cats, Tar, Onyx, Snow, milk, shaving cream, hair

Step 1: Categorize your items (in this case, “things that are black” and “things that are white”):
Black: Coal, Tar, Onyx
White: Snow, Milk, Shaving Cream
Can be both: Cats, hair

Step 2: Draw a rectangle and label it. For this sample question, label the rectangle “Black and/or white things.”

Step 3: Draw two or three circles according to how many categories you have. There are two categories in the sample question: “black” and “white”, so draw two circles. Make sure the circles overlap.

Step 4: Write the items that are in the intersection {cats, hair] in the space where the circles overlap.
Draw a Venn Diagram of A ∩ B
That’s it!
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Draw a Venn Diagram for A ∪ B : Overview


A Union (∪) is when items are in some or all categories. For example, let’s say you wanted to make a Venn diagram for categories of “black things” and “white things”. Your list of items is: Coal, Cats, Tar, Onyx, Snow, milk, shaving cream, and hair.
A union is written (the “mathy way”) as:
Black ∪ White = {Coal, Cats, Tar, Onyx, Snow, milk, shaving cream, hair}. The items that are a union (black, white, or could be both) are all of the items listed: Coal, Cats, Tar, Onyx, Snow, milk, shaving cream, hair.
But how would you put that in a diagram? The answer is to use circles to display each category; the circles overlap where the categories overlap.

Sample problem: Draw a Venn Diagram for A ∪ B (Union) for household gadgets that are electronic and/or non-electronic:
Vacuum, Mop, Television, Duster, Toothbrush, Hairdryer, Lawn Mower.

Step 1: Categorize your items (in this case, household gadgets):
Electronic: Vacuum, Television, Hairdryer.
Non-Electronic: Mop, Duster.
Both: Toothbrush, Lawn Mower.

Step 2: Draw a rectangle and label it. For this sample problem, label it “Household gadgets.”

Step 3: Draw circles according to how many categories you have. There are two categories in the sample problem: “electronic” and “non-electronic”, so draw two circles. Make sure the circles overlap.

Step 4: Write the items in the relevant circle. If items fit both categories, write those where the circles overlap.
Draw a Venn Diagram for A ∪ B

That’s it!

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Draw a Venn Diagram in Statistics: Easy Steps was last modified: October 20th, 2015 by Andale

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