1. 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

2. Naming Venn Diagrams We use set notation to name regions of a Venn diagram.

3. Naming Venn Diagrams cont. Example: Name r 2.

4. 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.

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

6. TV marketing survey cont. The universal set contains three subsets. Condition (a): there are 3 people in

7. TV marketing survey cont. Condition (b): there are 14 people in

8. TV marketing survey cont. Condition (c): 18 have not been counted in Condition (d): 8 people want to see weekday reality shows, so 5 people have not been counted in

9. 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}.

10. 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 n( W R ) = 13 + 4 = 17

11. Contradictions in Survey Problems A survey problem may contain contradictory information. Example: What web browsers are used by a certain sample of people?

12. 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).

13. 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 a) b)