Report

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 r4 B A r1 A B We use set notation to name regions of a Venn diagram. Naming Venn Diagrams cont. Example: Name r2. r2 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 • Condition (d): 8 people want to see weekday reality shows, so 5 people have not been counted in W R. E. 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 n( W ’ R ’) = 13 + 4 = 17 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 a) b) M A . D.