2. Welcome to Interactive Chalkboard Mathematics: Applications and Concepts, Course 3 Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc., Cincinnati, Ohio 45202 Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

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4. Contents Lesson 9-1Histograms Lesson 9-2Circle Graphs Lesson 9-3Choosing an Appropriate Display Lesson 9-4Measures of Central Tendency Lesson 9-5Measures of Variation Lesson 9-6Box-and-Whisker Plots Lesson 9-7Misleading Graphs and Statistics Lesson 9-8Matrices

5. Lesson 1 Contents Example 1Draw a Histogram Example 2Interpret Data Example 3Compare Two Sets of Data

6. Example 1-1a 2 II 81-100 061-80 2 II41-60 8IIII III21-40 7IIII II 1-20 FrequencyTallyCaffeine (mg) Caffeine Content of Certain Types of Tea FOOD The frequency table below shows the amount of caffeine in certain types of tea. Draw a histogram to represent the data.

7. Example 1-1a Step 1Draw and label a horizontal and vertical axis. Include a title. Step 2Show the intervals from the frequency table on the horizontal axis. Step 3For each caffeine interval, draw a bar whose height is given by the frequencies. Answer:

8. Example 1-1b FOOD The frequency table below shows the amount of caffeine in certain drinks. Draw a histogram to represent the data. 7 IIII II151-200 6 IIII I101-150 4IIII 51-100 3III 0-50 FrequencyTallyCaffeine (mg) Caffeine Content of Certain Types of Drink

9. Example 1-1b Answer:

10. Example 1-2a WEATHER How many months had 6 or more days of rain? Three months had 6 to 7 days of rain, and one month had 8 to 9 days of rain. Answer: Therefore, 3 + 1 or 4 months had 6 or more days of rain.

11. Example 1-2b WEATHER How many months had 6 or more days of snow? Answer: 4 months

12. Example 1-3a GRADES Determine which test had the greater number of students scoring 86 or higher. On test 1, 6 + 14 + 4 or 24 students scored 86 or higher. Answer: A greater number of students scored 86 or higher on test 2. On test 2, 16 + 6 + 4 or 26 students scored 86 or higher.

13. Example 1-3b Answer: test 1 GRADES Determine which test had the greater number of students scoring 70 or higher.

14. End of Lesson 1

15. Lesson 2 Contents Example 1Draw a Circle Graph Example 2Use Circle Graphs to Interpret Data Example 3Use Circle Graphs to Interpret Data

16. Example 2-1a TORNADOES The table shows when tornadoes occurred in the United States from 1999 to 2001. Make a circle graph using this information. 11%October-December 21%July-September 53%April-June 15%January-March Tornadoes in the United States, 1999-2001 Source: spc.noaa.gov/

17. Example 2-1a Step 1There are 360  in a circle. So, multiply each percent by 360 to find the number of degrees for each section of the graph. Jan – Mar: Apr – Jun: Jul – Sept: Oct – Dec:

18. Example 2-1a Answer: Step 2Use a compass to draw a circle and a radius. Then use a protractor to draw a 54  angle. This section represents January – March. From the new radius, draw the next angle. Repeat for each of the remaining angles. Label each section. Then give the graph a title.

19. Example 2-1b HURRICANES The table shows when hurricanes or tropical storms occurred in the Atlantic Ocean during the hurricane season of 2002. Make a circle graph using this information. 8%October 64%September 21%August 7%July PercentMonth Hurricanes in the United States, 2002 Source: nhc.noaa.gov/

20. Example 2-1b Answer:

21. Example 2-2a BASKETBALL Make a circle graph using the information in the histogram below.

22. Example 2-2a Step 2Find the ratio that compares the number in each point range to the total number of players. Round to the nearest hundredth. Step 1 Find the total number of players.

23. Example 2-2a Step 3Use these ratios to find the number of degrees of each section. Round to the nearest degree if necessary. Step 4Use a compass and protractor to draw a circle and the appropriate sections. Label each section and give the graph a title. Write the ratios as percents.

24. Example 2-2a Answer:

25. Example 2-2b FOOTBALL Make a circle graph using the information in the histogram below.

26. Example 2-2b Answer:

27. Example 2-3a Use the circle graph to describe the makeup of the average game scores of the 25 top-scoring basketball players.

28. Example 2-3a Sample answer: Almost of the players had average game scores between 11.1 and 15 points. Fewer than had average game scores greater than 17 points.

29. Example 2-3b Use the circle graph to describe the makeup of the average game scores of the 10 top-scoring football players. Sample answer: More than one half of the players had game scores between 0 and 15. Ten percent had scores greater than 24.

30. End of Lesson 2

31. Lesson 3 Contents Example 1Choose an Appropriate Display Example 2Choose an Appropriate Display

32. Example 3-1a FARMS The table shows farm acres in Maine. Choose an appropriate type of display for this situation. Then make a display. 2.5%1,000 or more acres 6.9%500-999 acres 43.8%100-499 acres 46.8%1-99 acres Farms in Maine by Size Source: ers.usda.gov This data deals with percents that have a sum of 100%. A circle graph would be a good way to show percents.

33. Example 3-1a Sample answer: circle graph

34. Example 3-1b TELEVISION The table shows the favorite type of television program of students at Walnut Junior High. Choose an appropriate type of display for this situation. Then make a display. Favorite Type of Television Program sitcom54% reality22% news10% game show 8% cartoon 6%

35. Example 3-1b Sample answer: circle graph

36. Example 3-2a SCHOOL The results of a survey of a group of students asked to give their favorite school subject are shown below. Choose an appropriate type of display for this situation. Then make a display. IIII Iother IIII IIEnglish IIII IIII IIscience IIII IIIhistory IIII IIII IIII IImath Favorite School Subject

37. Example 3-2a In this case, there are specific categories. If you want to show the specific number, use a bar graph or a pictograph. Sample answer: bar graph

38. Example 3-2b SCHOOL The results of a survey of a group of students asked to give their favorite hobby are shown below. Choose an appropriate type of display for this situation. Then make a display. HobbyNumber of students reading10 sports 5 listening to music10 photography 7 other18

39. Example 3-2b Sample answer: bar graph

40. End of Lesson 3

41. Lesson 4 Contents Example 1Find Measures of Central Tendency Example 2Using Appropriate Measures Example 3Using Appropriate Measures

42. Example 4-1a Find the mean, median, and mode of the set of data. 4, 16, 32, 19, 27, 32 Mean Median Arrange the numbers in order from least to greatest. 41619273232 ModeThe data has a mode of 32. Answer: mean: 21.7; median: 23; mode: 32

43. Example 4-1b Find the mean, median, and mode of the set of data. 3, 5, 3, 7, 6, 4 Answer: mean: 4.7; median: 4.5; mode: 3

44. Example 4-2a OLYMPICS What is the mean, median, and mode of the data in the table below? Gold Medals Won by the United States at the Winter Olympics, 1924-2002 Event Gold Medals Event Gold Medals Alpine skiing10Luge 2 Bobsleigh 6Short track speed skating 3 Cross country 0Skeleton 3 Figure skating13Ski jumping 0 Freestyle skiing 4Snowboarding 2 Ice hockey 3Speed skating26

45. Example 4-2a Mean The mean is 6 medals. MedianArrange the numbers from least to greatest. 0, 0, 2, 2, 3, 3, 3, 4, 6, 10, 13, 26 The median is the middle number or 3 medals. ModeThere is one mode, 3. Answer: mean: 6; median: 3; mode: 3

46. 12Ethiopia 12Brazil 74Romania 97Japan 101Finland 102Australia 150Hungary 136Sweden 179Italy 188France 180Great Britain 872United States Gold Medals (1896-2002 Summer)Country Source: infoplease.com Example 4-2b OLYMPICS What is the mean, median, and mode of the data in the table at the right? Answer: mean: 175.25; median: 119; mode: 12

47. Example 4-3a OLYMPICS Which measure of central tendency is most representative of the data in the table below? Gold Medals Won by the United States at the Winter Olympics, 1924-2002 Event Gold Medals Event Gold Medals Alpine skiing10Luge 2 Bobsleigh 6Short track speed skating 3 Cross country 0Skeleton 3 Figure skating13Ski jumping 0 Freestyle skiing 4Snowboarding 2 Ice hockey 3Speed skating26

48. Example 4-3a Answer: The median and the mode; the mean is affected by the extreme value of 26. The mode is the same as the median. So, both the median and the mode are good choices.

49. 12Ethiopia 12Brazil 74Romania 97Japan 101Finland 102Australia 150Hungary 136Sweden 179Italy 188France 180Great Britain 872United States Gold Medals (1896-2002 Summer)Country Source: infoplease.com Example 4-3b Which measure of central tendency is most representative of the data in the table below? Answer: The median; the mean is affected by the extreme value of 872 and the mode is much lower than the rest of the data.

50. End of Lesson 4

51. Lesson 5 Contents Example 1Find Measures of Variation Example 2Find Measures of Variation Example 3Find Measures of Variation Example 4Find Outliers

52. 91.3Portland 91.3Boston 91.6Indiana 93.8Orlando 95.4New Jersey 96.1Charlotte 97.8L.A. Lakers 101.1Sacramento 102Minnesota 109Dallas Points ScoredTeam Points Scored by Top Ten Teams During the NBA Playoffs, 2002 Source: nba.com Example 5-1a BASKETBALL Find the range of the scores in the table at the right. The greatest number of scores is 109. The least number of scores is 91.3. Answer: The range is 109 – 91.3 or 17.7 points.

53. 0.231Santiago 0.238Sanders 0.250Aurilia 0.276Kent 0.290Lofton 0.304Bell 0.407Snow 0.471Bonds 0.500Rueter Batting AveragePlayer Giants Batting Average Against Anaheim in the World Series 2002 Source: infoplease.com Example 5-1b BASEBALL Find the range of the batting averages in the table at the right. Answer: 0.269

54. 91.3Portland 91.3Boston 91.6Indiana 93.8Orlando 95.4New Jersey 96.1Charlotte 97.8L.A. Lakers 101.1Sacramento 102Minnesota 109Dallas Points ScoredTeam Points Scored by Top Ten Teams During the NBA Playoffs, 2002 Source: nba.com Example 5-2a BASKETBALL Find the median and the upper and lower quartiles of the scores in the table at the right.

55. Example 5-2a Arrange the numbers in order from least to greatest. 91.3 91.3 91.6 93.8 95.4 96.1 97.8 101.1 102 109 lower quartilemedianupper quartile Answer: The median is 95.75, the lower quartile is 91.6, and the upper quartile is 101.1.

56. 0.231Santiago 0.238Sanders 0.250Aurilia 0.276Kent 0.290Lofton 0.304Bell 0.407Snow 0.471Bonds 0.500Rueter Batting AveragePlayer Giants Batting Average against Anaheim in the World Series 2002 Source: infoplease.com BASEBALL Find the median and the upper and lower quartiles of the batting averages in the table at the right. Example 5-2b Answer: median: 0.290; upper quartile: 0.407; lower quartile: 0.250

57. 91.3Portland 91.3Boston 91.6Indiana 93.8Orlando 95.4New Jersey 96.1Charlotte 97.8L.A. Lakers 101.1Sacramento 102Minnesota 109Dallas Points ScoredTeam Points Scored by Top Ten Teams During the NBA Playoffs, 2002 Source: nba.com BASKETBALL Find the interquartile range of the scores in the table at the right. Example 5-3a Answer: :

58. 0.231Santiago 0.238Sanders 0.250Aurilia 0.276Kent 0.290Lofton 0.304Bell 0.407Snow 0.471Bonds 0.500Rueter Batting AveragePlayer Giants Batting Average against Anaheim in the World Series 2002 Source: infoplease.com Example 5-3b BASEBALL Find the interquartile range of the batting averages in the table at the right. Answer: 0.157

59. Items Sold at Football Game Concession Stand ItemNumber Sold Colas196 Diet colas 32 Water 46 Coffee 18 Candy bars 39 Hotdogs 23 Hamburgers 16 Chips 41 Popcorn 24 Example 5-4a CONCESSION SALES Find any outliers for the data in the table at the right.

60. Example 5-4a First arrange the numbers in order form least to greatest. 1618232432394146196 32 Multiply the interquartile range, 23, by 1.5. Find the limits for the outliers. Subtract 34.5 from the lower quartile. Add 34.5 to the upper quartile. Answer: The limits for the outliers are –14 and 78. The only outlier is 196.

61. Example 5-4b BOOKSTORE SALES Find any outliers for the data in the table below. Items Sold at School Bookstore ItemNumber Sold Pens35 Pencils15 Erasers20 Candy bars93 Folders17 School pennants18 Calculators 2 Answer: 93

62. End of Lesson 5

63. Lesson 6 Contents Example 1Draw a Box-and-Whisker Plot Example 2Interpret Data Example 3Compare Data

64. Example 6-1a POPULATION Use the data in the table at the right to draw a box-and-whisker plot. 13.5Manila 14.4Cairo 16.2Los Angeles 17.9Osaka 17.9Bombay 17.9Sao Paulo 19.8Mexico City 19.9Seoul 20.2New York 34.8Tokyo Population (millions)City World’s Most Populous Cities Source: Time Almanac

65. Step 1Draw a number line that includes the least and greatest number in the data. Step 2Mark the extremes, the median, and the upper and lower quartile above the number line. Since the data have an outlier, mark the greatest value that is not an outlier. median Example 6-1a Step 3Draw the box and whiskers. Answer: Least valuelower quartile upper quartile Greatest value that is not an outlier outlier

66. Example 6-1b POPULATION Use the data in the table below to draw a box-and-whisker plot. 1.2Dallas 1.2San Diego 1.3Phoenix 1.5Philadelphia 2.0Houston 2.9Chicago 3.7Los Angeles 8.0New York Population (in millions)City Most Populated U.S. Cities Source: infoplease.com

67. Example 6-1b Answer:

68. Example 6-2a WATERFALLS What does the length of the box-and- whisker plot below tell you about the data? Answer: Data in the second quartile are more spread out than the data in the third quartile. You can see that data in the fourth quartile are the most spread out because the whisker is longer than other parts of the plot.

69. Example 6-2b EXERCISE What does the length of the box-and- whisker plot below tell you about the data? Answer: Data in the second quartile are less spread out than the data in the third quartile. You can see that data in the third quartile are the most spread out because the box is longer than other parts of the plot.

70. A August temperatures were greater than those in April. B The temperatures were more spread out in April than in August. C Most April temperatures were above 25  C. D Most August temperatures were above 28  C. Example 6-3a MULTIPLE-CHOICE TEST ITEM Use the box-and- whisker plots below to determine which statement is not true.

71. Example 6-3a Read the Test Item You need to study the box-and-whisker plot. Solve the Test Item Most of the April temperatures were not above 25  C. The answer is C. Check to make sure A, B, and D are true. Answer: C

72. Example 6-3b MULTIPLE-CHOICE TEST ITEM Use the box-and- whisker plots below to determine which statement is not true. A July temperatures were mostly greater than those in May. B The temperatures were more spread out in July than in May. C Most May temperatures were above 50  F. D Most July temperatures were above 70  F. Answer: B

73. End of Lesson 6

74. Lesson 7 Contents Example 1Identify a Misleading Graph Example 2Identify Different Uses of Statistics Example 3Identify Different Uses of Statistics

75. Example 7-1a TELEVISIONS Which graph below could be used to indicate a greater difference in number of televisions? Explain.

76. Example 7-1a Both graphs show the order from greatest to least number of televisions per 1,000 people as Chili, Saudi Arabia, China, and Indonesia. However, the intervals in graph B represent 200 to 300 instead of 0 to 600 like graph A. Answer: Graph B shows a greater difference in televisions.

77. Example 7-1b SCHOOL Which graph below could be used to show a greater difference in favorite classes? Answer: Graph B because the interval does not start at 0.

78. Example 7-2a GYMNASTICS The scores for girls on a team competing on vault at a meet are 8.3, 8.5, 8.5, 8.8, 9.0, and 9.2. Find the mean, median, and mode of the vault scores. Median Mode Mean 8.5 Answer:The mean is 8.72, the median is 8.65, and the mode is 8.5. or about 8.72 or 8.65

79. Example 7-2b FIGURE SKATING The scores for girls on a team competing in the short program are 5.2, 5.5, 5.5, 5.9, 5.8, and 6.0. Find the mean, median, and mode of the scores. Answer: mean: 5.65; median: 5.65; mode: 5.5

80. Example 7-3a GYMNASTICS The scores for girls on a team competing on vault at a meet are 8.3, 8.5, 8.5, 8.8, 9.0, and 9.2. Which average would the team use to make its results look the best? Explain. A gymnastics team would most likely want to show the highest average in scores. The mean shows the highest event score, 8.72. Answer: Mean; it shows a higher event score.

81. Example 7-3b FIGURE SKATING The scores for girls on a team competing in the short program are 5.2, 5.5, 5.5, 5.9, 5.8, and 6.0. Which average would the team use to make its results look the best? Explain. Answer: Mean or median; both are 5.65 and show the highest average score.

82. End of Lesson 7

83. Lesson 8 Contents Example 1Identify Dimensions and Elements Example 2Add and Subtract Matrices Example 3Add and Subtract Matrices Example 4Add and Subtract Matrices

84. Example 8-1a Answer: The matrix has 3 rows and 3 columns. The dimensions of the matrix are 3 by 3. The circled element is in the second row and the first column. State the dimensions of. Then identify the position of the circled element.

85. Example 8-1b Answer: 2 by 3; first row, third column State the dimensions of. Then identify the position of the circled element.

86. Example 8-2a Answer: If there is no sum, write impossible. Find.

87. Example 8-2b Answer: If there is no sum, write impossible. Find.

88. Example 8-3a The first matrix has 2 rows and 2 columns. The second matrix has 1 row and 1 column. Answer: Since the matrices do not have the same dimensions, it is impossible to subtract them. If there is no difference, write impossible. Find.

89. Example 8-3b Answer: impossible If there is no difference, write impossible. Find.

90. Example 8-4a If there is no difference, write impossible. Find.

91. Example 8-4a Answer:

92. Example 8-4b Answer: If there is no difference, write impossible. Find.

93. End of Lesson 8

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