Section 4

Survey Problems

Objectives:

• Label sets in Venn diagrams with various names • Use Venn diagrams to solve survey problems • Understand how to handle contradictory information in survey problems

Naming Venn Diagrams

r

4

A r

1  

A B

  We use set notation to name regions of a Venn diagram.

Naming Venn Diagrams cont.

Example: Name r 2 .

r

2 

A B



C



Survey Problems

• When we collect and organize data into sets, we may also want to analyze the information.

• These types of problems are called

survey problems

.

• Example: A television network wants to determine how many people like to watch TV on the weekend but prefer not to see reality shows.

Survey Problems cont.

The television network conducted a market survey and obtained the following information on viewing habits.

TV marketing survey cont.

The universal set contains three subsets.

• Condition (a): there are 3 people in

W E R

.

TV marketing survey cont.

• Condition (b): there are 14 people in

W E

.

TV marketing survey cont.

• Condition (c): 18 have not been counted in

R E

.

• Condition (d): 8 people want to see weekday reality shows, so 5 people have not been counted in

W R

.

TV marketing survey cont.

• • Condition (e): there are 12 more members in W, 4 more in E, and 14 more in R.

Condition (h): there are 13 people outside {W, R, E}.

• • TV marketing survey cont.

Do not want to see reality shows: 12 + 11 + 4 + 13 = 40 Prefer to watch TV on weekend: 14 + 18 + 4 + 13 = 49 • Solution: The number of people who like to watch TV on the weekend but prefer not to see reality shows is

Contradictions in Survey Problems

• A survey problem may contain contradictory information.

• Example: What web browsers are used by a certain sample of people?

Contradictions in Survey Problems cont.

• • Condition (a): 212 have not been counted in W.

Condition (b): 374 have not been counted in I .

• Solution: 212 + 374 = 586 use only one of the two browsers which contradicts (d).

Data in Tabular Form

A company sells Pilates videos and surveys 180 potential customers with the following results.

Via Access Code = web download of video

(a) Find the number of elements in (b) Find the number of elements in

M A

 .

D

.

a) b)