Course: Math Literacy Aim: Solving Problems/Surveys w/Venn Diagrams and Sets Do Now: Aim: How do we use Venn Diagrams to visualize survey results. Would

Course: Math LiteracyAim: Solving Problems/Surveys w/Venn Diagrams and Sets

Do Now:

Aim: How do we use Venn Diagrams to visualize survey results.

Would you be willing to donate blood?

Would you be willing to help serve a free breakfast to blood donors?


Survey Results

BA

A = set of blood donorsB = set of breakfast servers

I II III

IV


Survey Results

BA I II III

IV

How 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?

and means intersection

or means union

not means complement

X Y X Y X Y


Solving Survey Problems

Solving Survey Problems

1. Use the survey’s description to define sets and draw a Venn diagram.

2. 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.

3. Use the completed Venn diagram to answer the problem’s questions.


Model Problem

In 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 statement

700 women agreed with the statement

If half the people surveyed were women,

a How many men agreed with the statement?

b. How many men disagreed with the statement?


Model Problem

1190 people agreed with the statement

700 women agreed with the statement

W(Women)

I II III

IV

A(Agree)U1.

2. Find cardinality of innermost region|W| = 1000 |A| = 1190 |W A| = 700

700

|U| = 2000

Region I = |W| – |W A| = 1000 – 700 = 300

300

Region III = |A| – |W A| = 1190 – 700 = 490

490

Region IV = |U| – Regions I, II, and III = 2000 – 1490 = 510

510


Model Problem

W(Women)

I II III

IV

A(Agree)U

700300 490510

3. a. 1190 of both sexes agree; 700 women agree: 1190 – 700 = 490 men agree.

a. How many men agreed with the statement?

b. How many men disagreed with the statement?

‘Job opportunities for women are not equal to those for men.’

b. 1000 men surveyed; 490 men agree; 510 disagree.


Solving 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:a) How many are taking only mathematicsb) only Englishc) only historyd) not taking any of these three courses


Model Problem

Understand the problemDevise a plan

Carry out the planLook back

U

M

H

E

Fill in the innermost region first

Work your way outward by subtraction until # elements in all regions is known

710

8

11

19 16

12

17100U

45M 41E

40H

|M E H| = 7|E H| = 17|M H| = 18|M E| = 15|H| = 40|E| = 41|M| = 4119+8+16+11+7+10+12 = 83


Model Problem

Sixty people were contacted and responded to a movie survey. The following information was obtained.

a. 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.


1. C = set of comedy loversD = set of drama loversS = set of science fiction lovers

Model Problem

|C| = 26|D| = 21|S| = 25

6 people liked comedies, dramas, and science fictionC D S = 6

C

S

D

65

7

4

9 3

10

11 people liked dramas and science fiction.

10 liked comedies and science fiction.

13 people liked comedies, and dramas

& 2.

|U| = 60

only C = 26 – 17 = 9

only D = 21 – 18 = 3

only S = 25 – 15 = 10


3. How many of those surveyed liked none of these categories of movies and how many liked only comedies.

Model Problem

C

S

D

65

7

4

9 3

10

60liked none: – (9 + 7 + 3 + 4 + 6 + 5 + 10)

|U| = 60

= 16

16


Model Problem

In 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.

a. How many respondents listened to classical music? b. How many listened to jazz?c. How many listened to both?d. How many listened to classical or jazz?e. How many listened to classical but not jazz?f. How many listened to jazz but not classical?g. Ho many listen to neither?h. How many were surveyed?

Classical

55 20 70

30

Jazz



Documents

Course: Math Literacy Aim: Solving Problems/Surveys w/Venn Diagrams and Sets Do Now: Aim: How do we use Venn Diagrams to visualize survey results. Would