6th Grade Math Textbook, Fundamentals

 &KDSWHU

8-9

Venn Diagrams

Objective To read and make Venn diagrams

Joy surveyed 25 music students on whether they
enjoyed playing guitar, piano, or drums. The table
shows the results of her survey.

How can Joy show the relationships among these
data sets? How many students enjoy playing only
guitar? Only piano? Only drums?

To show the relationships among the data sets,

you can use a Venn diagram. A

is a group of two or three overlapping circles,

each circle representing a single data set.

Draw and label three overlapping circles,

one to represent each instrument.

Find the region where the three circles

overlap. This region represents the 2 students

who enjoy playing all three instruments.

Write 2 in this region.

Four students enjoy playing both piano and

drums, but 2 of them like all three. So subtract

those from 4. Write 2 in the region shared by the

circles labeled piano and drums.

Three students enjoy playing guitar and drums, but

2 of them enjoy all three instruments. So subtract

those from 3. Write 1 in the region shared by the

circles labeled guitar and drums.

Three students enjoy playing guitar and piano, but

2 of them enjoy all three instruments. So subtract

those from 3. Write 1 in the region shared by the

circles labeled guitar and piano.

Ten students enjoy drums, but 2 like all three types, 2 enjoy piano and drums,

and 1 enjoys guitar and drums. So subtract (2  2 1), or 5, from 10 to find

the number who enjoy drums only. Write 5 in the region labeled drums.

Nine students enjoy piano, but 2 like all three types, 2 enjoy piano and drums,

and 1 enjoys piano and guitar. So subtract (2  2  1), or 5, from 9 to find the

number who enjoy drums only. Write 4 in the region labeled piano.

Fourteen students enjoy guitar, but 2 like all three types, 1 enjoys guitar and

piano, and 1 enjoys guitar and drums. So subtract (2  1  1), or 4, from 14 to

find the number who enjoy drums only. Write 10 in the region labeled guitar.

So the Venn diagram above represents the relationship among the data sets.

Venn diagram

Guitar

Drums

 Piano





 





Survey Questions Number ofStudents

How many enjoy playing

guitar?^14

How many enjoy playing

piano?^9

How many enjoy playing

drums?^10

How many enjoy playing

guitar and piano?^3

How many enjoy playing

guitar and drums?^3

How many enjoy playing

piano and drums?^4

How many enjoy playing

all three instruments?^2