3.3. Create a pie chart that defines the distribution (percentage) of various areas of the oceans around the globe. Pacific: 179.

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1 Chapter 3 Bar and Pie Graphs Problems 3.1. Nutritionists recommend the following proportion for the total daily food intake: 25% morning breakfast, 15% second breakfast, 45% lunch, and 15% dinner. Build a bar chart showing this proportion. (You can use Microsoft Word or Excel.) 3.2. Nutritionists recommend the following proportion for the total daily food intake: 25% morning breakfast, 15% second breakfast, 45% lunch, and 15% dinner. Build a pie chart showing this proportion. (You can use Microsoft Word or Excel.) 3.3. Create a pie chart that defines the distribution (percentage) of various areas of the oceans around the globe. The world consists of four oceans: Pacific: million km 2 Atlantic: 93.4 million km 2 Indian: 74.9 million km 2 Arctic: 13.1 million km Create a pie chart for the distribution of Earth s landmass in percentage if: Forest: 57 million km 2 Steppe: 24 million km 2 Tundra, deserts, marsh: 54 million km 2 41

2 Arable land: 15 million km The table shows the number of students in the classroom who came from different countries of the world. Russia USA Great Brittan Canada Which of the diagrams accurately reflects the data in the table? students have taken a math test. 30 people s scores were rated good, and 20 students scores were rated excellent. The number of students who did not pass an exam is three times less than those who did. Which of the following diagrams correctly reflects the results of the exam? 42

3 3.7. The pie chart shows the results of a math test, which was taken by 400 students. Determine the number of students who received scores of excellent, good, pass, and fail The pie chart shows the results of a math test. Determine the number of students who received scores of excellent, good, pass, and fail The pie chart shows the results of a math test. Determine the number of students who received scores of excellent, good, pass, and fail if the number of the students with excellent and fail scores is equal to 325 and the number of students who received good scores is 45% greater than the pupils with fail scores. 43

4 3.10. А diagram in the figure below shows the number of sales in Store #1 and #2 during four months. Which store had more sales from January to April? A bar chart in the figure below shows the number of sales of identical toys in two different stores (#1 and #2) during four months. One toy price is equal to seven dollars in Store #1 and five dollars in Store #2. Which store has more income? 44

5 3.12. What should be the number of sales in Store #1 if the ratio of total sales during four months in Store #2 to #1 is equal to 1.5? Two brothers opened stores that sell electronics. The bar graph shows sales (in percentage) for both stores during four months (January sales are taken as 100% in both stores). However, the first store graph shows sales change in comparison with January, and the second store graph shows sales change in comparison with the previous month. Which of the stores has more profit after four months of work? The profit of the store during fifteen years is expressed with the help of the bar graph below. Find the profit of the store during 12-th year and the total profit after 12 years. 45

6 3.15. Four candidates participate in the presidential elections. The preliminary survey indicates the following distribution: the first candidate received 28% of the vote, the second candidate received 32% of the vote, the third candidate received 80% of the votes that received candidate #2, and the fourth candidate received the rest of the votes. Build a pie chart that demonstrates the relationship between the percentages of votes for all candidates Four candidates participate in an election. The preliminary survey indicates the following distribution: the first candidate received 28% of the vote, the second candidate received 25% of the vote, the third candidate received 20% more votes than candidate #2, and the fourth candidate received the rest of the votes. Build a pie chart that demonstrates the relationship between the percentages of votes of all candidates The table and bar chart below show the results of the math test in class A and class B. The horizontal axis on the bar chart represents the number of students that received a particular score, on the vertical axis the score value. Find the average score for class A and class B. Which score is higher? 46

7 Number of Students A (Score in percent) B (Score in percent) The graph below shows test results of several student groups. Group A includes 35 students, group B has 30 students, group C comprises 25 people, and there are 40 students in group D. Using the data and bar graph, determine the average percentage of students with excellent, good, and satisfactory grades. 47

8 3.19. The bar graph below shows the number N of tickets that were sold in the theatre during one week. Find all combinations of possible days that correspond with ticket sales equal to 1,800. For example, 600 tickets were sold for days #1 and # Gas consumption (town and country) per 100 km for four cars of different companies is shown in the bar graph. Assuming that the annual average of kilometers driven per year in the city and in the country is the same, determine which car is more economical Gas consumption (town and country) per 100 km for four cars of different companies is shown in the bar graph. Assuming that the annual average of kilometers driven per year in the country two times more than in the city, determine which car is more economical. 48

9 3.22. The bar graph below shows energy consumption over the last two years. The solid line determines the mean monthly outside temperature. Explain a relationship between temperature and power consumption. Calculate the approximate values of the temperatures T1 and T2 averaged over season #1 (November, January, and March) as well as season #2 (May, July, and September). Also calculate the corresponding average values of electricity power consumption G1 and G2 over seasons #1 and #2, respectively The bar graph below shows the number of students as a percentage of the total number of younger Canadian school pupils 49

10 whose knowledge of mathematics assessed above baseline. What is the main conclusion that can be made from this graph? students took a quiz that included 5 math problems. 10 pupils solved all problems, 30 students solved 4 problems, 50 schoolchildren gave a right answer for 3 questions, 2 problems were solved correctly by 25 people, and 10 students gave a right answer for one question. Based on these data, create a bar chart that characterizes how many students did not solve one, two, three, four, and five problems students took a quiz that includes 5 math problems. 10 pupils solved all problems, 30 students solved 4 problems, 50 schoolchildren gave a right answer for 3 questions, 2 problems were solved correctly by 25 people, and 10 students gave a right answer for one question. Based on these data, create a bar chart that characterizes how many students did not solve at least one, two, three, four, and five problems The chart below shows the income (arbitrary units) in four different stores. Estimate which income is more: the total for four months in the store with the highest total revenue, or total in all the stores in one month where the total revenue is the greatest. 50

11 3.27. The unemployment rate in several key provinces in Canada is shown in the diagram below. Determine the unemployment rate X in Ontario if the average unemployment rate for all provinces is equal to The number of flyers distributed from Monday to Sunday among homeowners is shown below, excluding Friday and Sunday. The total number of delivered flyers is 207. It is known that 3 more flyers 51

12 were distributed on Friday than on Sunday. Determine the number of flyers distributed on Friday and Sunday The number of flyers distributed from Monday to Sunday among homeowners is shown in below, excluding Friday and Sunday. The total number of delivered flyers is 209. It is known that 1.3 times more flyers were distributed on Friday than on Sunday. Determine the number of flyers distributed on Friday and Sunday The figure below shows two pie charts that define the power of the signal received by the car radio antenna. The charts determine the received signal, depending on the car position relative to cardinal directions. Explain which of the two diagrams is more preferable. 52

13 3.31. An antenna receives radio signals from different directions. The following table shows the signal levels (in arbitrary units) taken from eight different directions. Which of the radial diagrams shown below correctly reflects the data in the table?

14 3.32. Radio antennas of two identical cars receive signals from the same transmitting tower. Signal power, depending on the car angle orientation, is shown in the figure. Find the angle between the cars The diagram below schematically presents the signal power received by a car s FM radio antenna as a function of an angle between the incoming signal direction and the orientation of the car as shown in the diagram. The car is located in the north-south direction as shown in the figure. Data are presented for two different models. Specify two features that characterize the received signals for different cars. 54

15 3.34. The diagram below shows the probability that a family has one, two, or three kids. The horizontal axis shows the number of children in the family, and the vertical shows the corresponding probability. On the basis of the chart, estimate an average number N of children in the family The diagram below shows the probability that a family has one, two, or three kids. The horizontal axis shows the number of children in the family, and the vertical shows the corresponding probability. On the basis of this chart, create a chart that reflects the probability that family has at least one, two, or three kids A math teacher summarized the results of the control work. The results are presented in a pie chart. Sector A (12%) corresponds to 55

16 the number of students with the highest score Excellent. Sector B (15%) corresponds to the number of pupils that have good results. Sector C (56%) corresponds to the number of students rated with score Pass. Finally, sector D (17%) corresponds with the number of students who did not take the test. Which of the following statements regarding the test results is wrong? a. More than half of the students received a score Pass. b. More than a quarter of students did not take the test. c. Less than 25 percent of students received a highest score. d. The number of students who received a score Pass, Good, or Excellent is more than half of the total number of pupils that took the test The number of student from grades five, six, seven, and eight who attend advanced math class is shown in the figure below. 56

17 Which statement is true regarding the students in advanced classes if the total amount of students is 360? a. There are no advanced students in grade five. b. The number of students in advanced grade eight is more than the number of students in advanced grade seven. c. More than half of the total amount of students is not from grade seven. d. The number of students from grade six is less than eighty-eight athletes from four countries participated in international competitions. The figures below show the distribution of athletes from different countries and the ratio of the winners to the total number of participants. Medalists came in second or third place. Participants are athletes who are not winners or medalists. Figure 1 Figure 2 57

18 Which statement is true? a. At least five winners are not from the United States. b. All athletes from the United States became winners. c. At least one athlete from China was a winner. d. At least five Russian athletes were winners The store sells toys of different sizes: large, medium, and small. The figure below shows the relationship between the number of different-sized toys. Determine the number of toys of each size if the total number of toys is The store sells toys of different sizes: large, medium, and small. Figure 1 shows the relationship between the number of differentsized toys. Figure 2 shows the number of different-colored toys. Figure 1 58

19 Figure 2 Which one of the following statements is true? a. There are no small, yellow toys. b. Some blue or red toys are medium sized. c. More than half of the total number of toys is blue and yellow. d. Green toys are not large There are one hundred employees in a company. Each employee knows at least one foreign language (English, French, or German). The following chart reflects the number of people who knows each language. The pie graph below reflects information about employees who know one, two, or three languages. 59

20 Determine the number of people who speak only English There are one hundred employees in a company. Each of employees knows at least one foreign language (English, French, or German). The following chart reflects the number of people who know each language. The pie graph reflects information about employees who know one, two, or three languages. 60

21 Determine the number of people who speak only French and English if two people know English and German but don t know French Figure 1 shows the relationship between the different-sized toys offered. Figure 2 demonstrates their color distribution. Figure 1 Figure 2 The total amount of toys is 200, green and blue toys are only medium sized, and red and yellow toys are not medium sized. Determine the number of green and yellow toys in figure The number of cars and their colors in the underground parking lot are shown in the bar graph below. Determine the number of white and silver cars if the total number of cars is 520 and the ratio of red cars to white cars is equal to the ratio of black cars to silver cars. 61

22 3.45. The number of cars and their colors in the underground parking lot are shown in the bar graph below. Determine the number of white and silver cars if the total number of cars equals 520 and the difference between the number of white and silver cars is equal to The number of cars and their colors in the underground parking lot are shown in the bar graph below. Determine the number of white and silver cars if the difference between the total number of vehicles and the total number of red, white, and brown cars is two hundred. The number of black and silver cars is equal to the number of red and white cars. 62

23 3.47. A shop sells shirts, sweaters, and hats of different sizes: A, B, C, and D. Figure 1 shows an item s size distribution. Figure 2 highlights the number of different goods. Figure 1 Figure 2 63

24 Which of the following statements is certainly not true? a. Goods of size D account for 25 percent of the total quantity of goods. b. All shirts and hats can be of the same size. c. All sweaters and hats may not be of the same size. d. The number of sweaters is more than the number of the size-a goods A shop sells shirts, sweaters, and hats of different sizes: A, B, C, and D. Figure 1 shows an item s size distribution. Figure 2 highlights the number of different goods. Figure 1 Figure 2 64

25 Which of the following statements may be true? a. All shirts can have the same size. b. All hats and sweaters are of the same size. c. All sweaters can be size A or B The figure below shows a four-way stop with cars #1, #2, #3, and #4 arriving at the intersection. A motorist approaching an allway stop is always required to come to a full stop (about three seconds) before the crosswalk. After a full stop has been made, vehicles usually have the right-of-way to proceed through the intersection in the order that they arrived at the intersection. Assuming that each car leaves the intersection 3 seconds after the previous one, estimate the time delay between the moment when the first car (in lane 1) arrived to the intersection and last car (in lane 4) left the intersection The figure below shows the four-way stop with the arrived cars. A motorist approaching an all-way stop is always required to come to a full stop before the crosswalk. After a full stop stop (about three seconds), vehicles usually have the right-of-way to proceed through the intersection in the order that they arrived at the intersection. According to the scenario presented in the figure below, estimate the time delay between the moment when the first car (in lane 1) arrived to the intersection and last car (in lane 4) left the intersection. 65

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