Probability and Statistics > Probability > How to Create an Euler Diagram

## Euler diagram: Overview

An Euler diagram is similar, but not the same as, a Venn diagram. While they both use circles to create diagrams, there’s a major difference: Venn diagrams represent an **entire set**, while Euler diagrams can represent a **part of a set.** A Venn diagram can have a shaded area to show an empty set. That area in an Euler diagram could simply be missing from the diagram altogether. Euler diagrams are difficult to draw by hand (a simple one is outlined below). You’re probably better off using software to create one like Smart Draw or Venn Master.

## Euler diagram: Steps

**Sample question:** Draw an Euler diagram to represent the following statements:

All wizards can do magic.

No lizards can do magic.

No wizard is a lizard.

Step 1: **Draw three circles to represent the three categories** (wizard, lizard, magic). Overlap them all (use a pencil or software so you can move the circles later):

Step 2: **Read the first statement and move the corresponding circle accordingly**. “All wizards can do magic” must mean that the entire wizard circle has to be inside the magic circle.

Step 2: **Read the second statement and move the corresponding circle accordingly**. “No lizards can do magic” must mean that the entire lizard circle has to be *outside* the magic circle.

Step 3: **Read the third statement and move the corresponding circle accordingly**. “No wizards are lizards” must mean that the entire lizard circle has to be *outside* the wizard circle. In this case, the graph already has the lizard circle outside the wizard circle, so we’re done!

Reference:

University of Kent . Retrieved October 19th, 2015.

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*Statistical concepts explained visually* - Includes many concepts such as sample size, hypothesis tests, or logistic regression, explained by Stephanie Glen, founder of StatisticsHowTo.

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