Presentation on theme: "Aim: How do we use Venn Diagrams to visualize survey results."— Presentation transcript:
1Aim: How do we use Venn Diagrams to visualize survey results. Do Now:Would you be willing to donate blood?Would you be willing to help serve a free breakfast to blood donors?
2Survey ResultsA = set of blood donorsB = set of breakfast serversABIIIIIIIV
3Survey ResultsBAand means intersectionor means unionIIIIIInot means complementIVHow many students are willing to donate blood?How many students are willing to help serve?How many students are willing to donate & help serve?How many students are willing to donate or help serve?How many students are willing to donate but not serve?How many students are willing to serve but not donate?How many students are neither will to donate nor serve?How many students are surveyed?
4Solving Survey Problems Use the survey’s description to define sets and draw a Venn diagram.Use the survey’s results to determine the cardinality for each region in the Venn diagram. Start with the intersection of the sets, then innermost region and work outward.Use the completed Venn diagram to answer the problem’s questions.
5Model ProblemIn a Gallup poll, 2000 US adults were selected at random and asked to agree or disagree with the following statement:‘Job opportunities for women are not equal to those for men.’1190 people agreed with the statement700 women agreed with the statementIf half the people surveyed were women,a How many men agreed with the statement?b. How many men disagreed with the statement?
61190 people agreed with the statement Model ProblemU1.1190 people agreed with the statementW(Women)A(Agree)IIIIII700 women agreed with the statement300700490510IV2. Find cardinality of innermost region|U| = 2000|W| = 1000|A| = 1190|W A| = 700Region I = |W| – |W A| = 1000 – 700 = 300Region III = |A| – |W A| = 1190 – 700 = 490Region IV = |U| – Regions I, II, and III = – 1490 = 510
7‘Job opportunities for women are not equal to those for men.’ Model Problem‘Job opportunities for women are not equal to those for men.’a. How many men agreed with the statement?b. How many men disagreed with the statement?UW(Women)A(Agree)IIIIII300700490510IV3. a of both sexes agree; 700 women agree: – 700 = 490 men agree.b men surveyed; 490 men agree; 510 disagree.
8Solving Problems with Venn Diagrams A survey of 100 randomly selected students gave the following information.45 students were taking mathematics41 students were taking English40 students were taking history15 were taking math and English18 were taking math and history17 were taking English and history7 were taking all three.Use a Venn Diagram to find:How many are taking only mathematicsonly Englishonly historynot taking any of these three courses
917 19 8 16 7 11 10 12 Model Problem U Understand the problem Devise a planCarry out the planLook backME1719816H71110= 83|H| = 40|M| = 41|M E| = 15|E| = 41|E H| = 17|M H| = 18|M E H| = 712Fill in the innermost region firstWork your way outward by subtractionuntil # elements in all regions is known
10Model ProblemSixty people were contacted and responded to a movie survey. The following information was obtained.6 people liked comedies, dramas, and science fiction. b. 13 people liked comedies, and dramas c. 10 liked comedies and science fiction d. 11 people liked dramas and science fiction e. 26 people liked comedies f. 21 people liked dramas g. 25 people liked science fiction.How many of those surveyed liked none of these categories of movies and how many liked only comedies.
117 9 3 6 4 5 10 Model Problem C = set of comedy lovers D = set of drama loversS = set of science fiction lovers|C| = 26& 2.|D| = 21|U| = 60|S| = 256 people liked comedies, dramas, and science fictionC D S = 611 people liked dramas and science fiction.CD710 liked comedies and science fiction.93613 people liked comedies, and dramas45only C = 26 – 17 = 910only D = 21 – 18 = 3only S = 25 – 15 = 10S
12Model Problem3. How many of those surveyed liked none of these categories of movies and how many liked only comedies.|U| = 60liked none:60– ( )= 16CD7936451016S
13How many respondents listened to classical music? 55207030JazzModel ProblemIn a survey of musical tastes, respondents were asked: Do you listen to classical music? Do you listen to jazz? The survey results are summarized above. Use the diagram to answer the following questions.How many respondents listened to classical music?How many listened to jazz?How many listened to both?How many listened to classical or jazz?How many listened to classical but not jazz?How many listened to jazz but not classical?Ho many listen to neither?How many were surveyed?