Section 2-2

1. Chapter 2 Frequency Distributions and Graphs Section 2-2 Organizing Data

2. Chapter 2 Frequency Distributions and Graphs Section 2-2 Exercise #7

3. The following data represent the color of men’s dress shirts purchased in the men’s department of a large department store. Construct a categorical frequency distribution for the data (W = white, BL = blue, BR = brown, Y = yellow, G = gray).

4. Class Tally f Percent W |||| |||| |||| | 16 32% BL |||| |||| ||| 13 26% BR |||| |||| 9 18% Y |||| | 6 12% G |||| | 6 12% 50 100% Construct a categorical frequency distribution for the data (W = white, BL = blue, BR = brown, Y = yellow, G = gray).

5. Chapter 2 Frequency Distributions and Graphs Section 2-2 Exercise #7

6. A survey taken in a restaurant shows the following number of cups of coffee consumed with each meal.

7. Class Bounds f cf 0 –0 .5 – 0.5 5 5 1 0.5 – 1.5 8 13 2 1.5 – 2.5 10 23 3 2.5 – 3.5 2 25 4 3.5 – 4.5 3 28 5 4.5 – 5.5 30 2 30 Construct an ungrouped frequency distribution.

8. Chapter 2 Frequency Distributions and Graphs Section 2-2 Exercise #11

9. The average quantitative GRE scores for the top 30 graduate schools of engineering are listed below. Construct a frequency distribution with six classes. Source: N.Y. Times Almanac.

10. 767 770 761 760 771 768 776 771 756 770 763 760 747 766 754 771 771 778 766 762 780 750 746 764 769 759 757 753 758 746 The average quantitative GRE scores for the top 30 graduate schools of engineering are listed below. Construct a frequency distribution with six classes. H= 780 L= 746 Range = 780 – 746 = 34 = 34  6 = 5.6 or 6 Width

11. Construct a frequency distribution with six classes. H= 780 L= 746 Range = 780 – 746 = 34 = 34  6 = 5.6 or 6 Width

12. Chapter 2 Frequency Distributions and Graphs Section 2-2 Exercise #13

13. The ages of the signers of the Declaration of Independence are shown below. (Age is approximate since only the birth year appeared in the source, and one has been omitted since his birth year is unknown.) Construct a frequency distribution for the data using seven classes. Source: The Universal Almanac

14. H= 70 L= 27 Range= 70 – 27 Width= 43  7 = 43 = 6.1 or 7 41 54 47 40 39 35 50 37 49 42 70 32 44 52 39 50 40 30 34 69 39 45 33 42 44 63 60 27 42 34 50 42 52 38 36 45 35 43 48 46 31 27 55 63 46 33 60 62 35 46 45 34 53 50 50 Construct a frequency distribution for the data using seven classes.

15. H= 70 L= 27 Range= 70 – 27 Width= 43  7 = 43 = 6.1 or 7 Limits Boundaries f cf 27 – 33 26.5 – 33.5 7 7 34 – 40 33.5 – 40.5 14 21 41 – 47 40.5 – 47.5 15 36 48 – 54 47.5 – 54.5 11 47 55 – 61 54.5 – 61.5 3 50 32 – 68 61.5 – 68.5 3 53 69 – 75 68.5 – 75.5 2 55 55 Construct a frequency distribution for the data using seven classes.

16. Appendix B Bayes’ Theorem Section B-1 Tree Diagram

17. Appendix B Bayes’ Theorem Section B-1 Example B-1

18. A shipment of two boxes, each containing six telephones, is received by a store. Box 1 contains one defective phone and box 2 contains two defective phones. After the boxes are unpacked, a phone is selected and found to be defective. Find the probability that it came from box 2.

19. STEP 1 Select the proper notation. Let A1represent box 1 and A2 represent box 2. Let D represent a defective phone and ND represent a phone that is not defective.

20. STEP 2 Draw a tree diagram and find the corresponding probabilities for each branch. The probability of selecting box 1 is , and the probability of selecting box 2 is . Since there is one defective phone in box 1, the probability of selecting a nondefective phone from box 1 is .

21. P ( D | A ) 2 P ( D | A ) 1 = = 2 1 6 6 1 1 P P ( ( A A ) ) = = 1 2 2 2 4 5 ND ND P P ( ( | | A A ) ) = = 2 1 6 6 Phone D Box A1 ND D A2 ND

22. STEP 3 Write the corresponding formula. Since the example is asking for the probability that, given a defective phone, it came from box 2, the corresponding formula is as shown

23. 2 1

24. Appendix B Bayes’ Theorem Section B-2

25. Appendix B Bayes’ Theorem Section B-2 Example B-2

26. Example B-2: On a game show, a contestant can select one of four boxes. Box 1 contains one $100 bill and nine $1 bills. Box 2 contains two $100 bills and eight $1 bills. Box 3 contains three $100 bills and seven $1 bills. Box 4 contains five $100 bills and five $1 bills. The contestant selects a box at random and selects a bill from the box at random. If a $100 bill is selected, find the probability that it came from box 4.

27. STEP 1 Select the proper notation. Let B1, B2, B3 and B4 represent the boxes and 100 and 1 represent the values of the bills in the boxes.

28. STEP 2 Draw a tree diagram and find the corresponding probabilities. The probability of selecting each box is , or 0.25. The probabilities of selecting the $100 bill from each box, respectively, are and . The tree diagram is shown in Figure B-3.

29. | | | | ( ( ( ( ) ) ) ) 100 100 100 100 B B B B 0 0 0 0 . . . . 5 3 2 1 P P P P = = = = 3 4 2 1 ( ) ( ) ( ( ) ) B 0 . 25 B 0 . 25 B B 0 0 . . 25 25 P = P P P = = = 4 1 3 2 | | | | ( ( ( ( ) ) ) ) 1 1 1 1 B B B B 0 0 0 0 . . . . 5 7 8 9 P P P P = = = = 4 3 1 2 Bill Box $100 Box 1 $1 $100 Box 2 $1 $100 Box 3 $1 $100 Box 4 $1

30. STEP 3 Using Bayes’ theorem, write the corresponding formula. Since the example asks for the probability that box 4 was selected, given that $100 was obtained, the corresponding formula is as follow

31. Chapter 2 Frequency Distributions and Graphs Section 2-4 Other Types of Graphs

32. Chapter 2 Frequency Distributions and Graphs Section 2-4 Exercise #1

33. The population of federal prisons, according to the most serious offenses, consists of the following. Make a Pareto chart of the population. Source: N.Y. Times Almanac

35. Chapter 2 Frequency Distributions and Graphs Section 2-4 Exercise #7

36. The data above represents the personal consumption expenditures for food for the United States (in billions of dollars). Draw a time series graph to represent the data. Source: The World Almanac and Book of Facts.

38. Chapter 2 Frequency Distributions and Graphs Section 2-4 Exercise #11

39. The assets of the richest 1% of Americans are distributed as follows. Make a pie chart for the percentages. Source: The New York Times.

40. Make a pie chart for the percentages.

41. Make a pie chart for the percentages.

42. Chapter 2 Frequency Distributions and Graphs Section 2-4 Exercise #15

43. The age at inauguration for each U.S. President is shown below. Construct a stem and leaf plot and analyze the data. Source: N.Y. Times Almanac.

44. Construct a stem and leaf plot and analyze the data. The majority of the Presidents were in their 50’s at inauguration.

45. Chapter 2: Frequency Distributions and Graphs Section 2.5Paired Data and Scatter Plots

46. Chapter 2: Frequency Distributions and Graphs Section 2.5Exercise #5

47. Height, x 485 511 520 535 582 615 616 635 728 841 No. ofStories, y 40 37 41 42 38 45 31 40 54 64 The data represent the heights in feet and the number of stories of the tallest buildings in Pittsburgh.Draw a scatter plot for the data and describe the relationship. Source: The World Almanac and Book of Facts.

48. Height, x 485 511 520 535 582 615 616 635 728 841 No. ofStories, y 40 37 41 42 38 45 31 40 54 64 100 80 60 40 20 0 No. of Stories 0 200 400 600 800 1000 Height

49. 100 80 60 40 20 0 No. of Stories 0 200 400 600 800 1000 Height There appears to be a positive linear relationship between the height of a building and the number of stories contained in the building.

50. Chapter 2: Frequency Distributions and Graphs Section 2.5Paired Data and Scatter Plots