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CHAPTER 11 Data Analysis GET READY 614 Math Link 616 11.1 Warm Up 617 11.1 Factors Affecting Data Collection 618 11.2 Warm Up 625 11.2 Collecting Data 626 11.3 Warm Up 635 11.3 Probability in Society 636 11.4 Warm Up 649 11.4 Developing and Implementing a Project Plan 650 s Math Link: Wrap It Up! 654 Graphic Organizer 655 Chapter 11 Review 656 Key Word Builder 660 Chapter 11 Practice Test 661 Challenge 663 Chapters 8–11 Review 664 Answers 671 Name: _____________________________________________________ Date: ______________ Get Ready Measures of Central Tendency sum of items number of items example: In the data set 1, 3, 4, 1, 5, 2, 4, 4, the mean is 3: 1 + 1 + 2 + 3 + 4 + 4 + 4 + 5 24 = =3 8 8 Mean: what most people call the average. Mean = ● lowest to highest Median: the middle number in a set of data that has been arranged in ascending order ● example: 43, 43, 45, 46, 47 has an odd number of data values. The middle number is 45, so 45 is the median. ● example: 1, 1, 2, 3, 4, 4, 4, 5 has an even number of data values. The median is halfway 3+ 4 = 3.5 between the two middle numbers, 3 and 4. Median = 2 Mode: the number that appears the most often in a set of data. ● example: In 1, 1, 2, 3, 4, 4, 4, 5, the mode is 4. ● A data set can have more than 1 mode. ● example: In 1, 3, 3, 6, 6, 10, the modes are 3 and 6. 1. Find the mean, median, and mode. a) 1, 3, 6, 2, 8, 5, 15, 15, 8 Mean = = sum of values number of values 1 + 3 + 6 + 2 + 8 + 5 + 15 + 15 + 8 = = Ascending order: Median = Mode = 614 MHR ● Chapter 11: Data Analysis b) 4.3, 4.5, 4.2, 5 Name: _____________________________________________________ Date: ______________ Calculating the Range The range tells you about the spread of the data. ● Range = highest value – lowest value ● example: 1, 1, 2, 3, 4, 4, 4, 5 Highest value = 5; lowest value = 1. The range is 5 – 1 = 4. 2. Find the range. a) 9, 8, 8, 3, 7 b) 16, 11, 7, 29, 31, 24, 18, 18, 18 Range = highest value – lowest value = – = Representing Data Circle graphs are best for comparing parts of a whole using percents. De Re lic d iou s De lic Go Fu iou n s Jo go nal M d ac int os h Varieties of Apples Sold ji 60 50 40 30 20 10 0 lde Number of Apples You can show data using graphs. Bar graphs are best for comparing data across different groups. Variety Line graphs are best for showing changes in data over time. Number of T-Shirts Pictographs are best for comparing data that can be easily counted. 50 40 30 20 10 0 T-Shirt Sales 1 2 3 4 5 6 7 Week Truong recorded the water flow from 3 taps on a line graph. a) Which tap flows the fastest? b) What is the approximate water flow in 2 min from Tap B? Volume (L) 3. Water Flow From Three Taps A 45 40 35 30 25 20 15 10 5 0 1 2 3 4 Time (min) B C Get Ready ● MHR 615 Name: _____________________________________________________ Date: ______________ Math Link Protecting and Managing Wildlife Elk Island National Park in Alberta is home to many ungulates. An ungulate is a mammal with hooves, such as plains bison, wood bison, moose, deer, and elk. The table shows data about the ungulates in the park. 1. Display the data on a bar graph. Then, display the data on a pictograph. For a bar graph: Choose a scale for the y-axis. Title and label both axes. Plot the categories along the x-axis. Draw bars for each ungulate. Add a title. Ungulate Approximate Total Park Count (2007 Fall Count) Plains bison 425 Wood bison 400 Elk 605 Moose 300 Deer 558 For a pictograph: Choose symbols for each category. Provide a key or a legend. Add a title. Complete the graph. y x 2. Which ungulate has the largest population? 3. a) The park has an area of 194 km2. What is the mean number of elk per square kilometre? Round your answer to the nearest whole number. number of elk = area = 616 /km2 MHR ● Chapter 11: Data Analysis b) What percent of the ungulate population do bison represent? Round your answer to the nearest percent. number of bison × 100 total number of ungulates Name: _____________________________________________________ Date: ______________ 11.1 Warm Up 1. The graph shows categories of books the Wong family signed out from the library. a) Approximately how many books in total did the Wong family sign out? b) Which category of book did the Wong family sign out most often? 2. The circle graph is another way to show the categories of books the Wong family signed out from the library. a) What percent of the books are Adventure or Sports? b) Is it possible that the Wong family signed out books from categories other than the ones shown? Circle YES or NO. Give 1 reason for your answer. _____________________________________________________________________________ 3. The mean of 40, 50, and 60 is . 4. A school has 400 students. If 40 students were surveyed, what percent of the school was surveyed? Sentence: _______________________________________________________________________ 11.1 Warm Up ● MHR 617 Name: _____________________________________________________ Date: ______________ 11.1 Factors Affecting Data Collection Link the Ideas When you do a survey, influencing factors can affect the data you collect: Literacy Link A survey collects opinions and/or information. ● bias: Does the question seem to show that one thing is better than another? ● use of language: Can people understand the question? ● ethics: Does the question ask about inappropriate things? ● cost: Does the study cost too much? ● time and timing: Is the survey being done at the right time? How long does it take to do the survey? ● privacy: Do people have the right to refuse to answer? Are the responses kept a secret? ● cultural sensitivity: Could the question offend people from different cultural groups? Literacy Link Ethics involve judgments of right and wrong. For example, cheating on a test is ethically wrong. Working Example 1: Identify Factors Affecting Data Collection Check each situation for influencing factors. Give 1 reason for each factor you find. a) A salesperson stands in front of a display of toothpaste. He asks every person buying toothpaste this question: What is your favourite brand of toothpaste? For what reason(s)? Solution Ask yourself, “Does the question seem to show that one kind of toothpaste is better than another?” Circle YES or NO. There is no bias. By standing in front of a toothpaste display, the salesperson can survey people who are buying toothpaste. Asking questions to gather information. 618 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ Date: ______________ b) A company sends free samples of sunscreen to every home in fall and winter. A survey asks people if they would use the sunscreen again. Solution Ask yourself, “Is this question being asked at the right time of year?” Circle YES or NO. People likely wear sunscreen during the fall and winter than (more or less) during the summer. So, fall and winter the best time for testing sunscreen. (are or are not) Asking people if they will use the product again assumes they use it. (did or did not) This may confuse people. The language is unclear. c) A grocery store employee does a telephone survey of people living within 10 km of the store. She asks what type of red meat people prefer. Solution Ask yourself, “Could this question offend some people?” Circle YES or NO. The question is biased. It assumes that all people eat Red meat is not acceptable to some people. This may be a sensitive question for some people. meat. d) A sales representative does a telephone survey. As she asks the question, the person receiving the call says, “I am not interested, thank you.” The sales representative responds, “Why not? Your input provides useful information.” She begins to repeat the survey question. Solution Ask yourself, “Does the person have the right to refuse to participate?” Circle YES or NO. The sales representative respect the person’s right to refuse to participate (did or did not) in the survey. Responses obtained under pressure may not truly represent the person’s opinion. 11.1 Factors Affecting Data Collection ● MHR 619 Name: _____________________________________________________ e) Date: ______________ Your school is under construction and is dusty and dirty. A survey is conducted about the environmental health of your school. The survey is done every 4 years. Solution Ask yourself, “Is the survey being conducted at a good time?” Circle YES or NO. This survey is poorly timed. The school is under construction so the results will be unfair. f) A salesperson sets up an online survey. The survey offers a free MP3 file download to everyone who completes the survey. The company has not bought the rights to the song. An ethical survey is honest and fair. Solution Ask yourself, “Is the survey ethical?” Circle YES or NO. The download is being stolen, which is wrong. Also, giving a reward for doing a survey is not ethical because the reward may change the way people respond. Kelly is selling school shirts to students in grades 8 to 12. She has 2 different kinds of shirts. She wants to know which shirt students like better. She asks the first 10 grade 12 students who come to school this question: Which one of these 2 shirts would you buy? The poster shows the results. Over 80% of students at Central High will buy Shirt B. A: $29.95 B: $49.95 a) Is the survey fair? Circle YES or NO. Give 2 reasons why or why not. ● __________________________________________________________________________ ● __________________________________________________________________________ b) What is 1 way to improve the survey? ___________________________________________________________________________ 620 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ Date: ______________ Working Example 2: Write Survey Questions Free of Influencing Factors A steel mill company conducts a survey about putting a new mill in a small community. Influencing factors affect how data are collected or the answers people give. The proposed mill will produce 250 jobs and economic benefits for your community. Are you in favour of having a forward-thinking steel mill in your community? YES NO a) What parts of the question help the steel mill get positive responses? Solution Ask yourself, “What parts of the article make the mill look like a good idea?” The first part says jobs would be . (created or taken away) Also, the question says the mill is “forward thinking.” The survey is biased in favour of the mill. b) Rewrite the question so it is free of influencing factors. has influencing factors Solution Are you in favour of having a steel mill in your community? For each question, list the influencing factors. Then, rewrite the question. a) Daniel is studying the population of polar bears in Hudson Bay. He writes this question: Do you think the senseless slaughter of polar bears should be stopped? YES NO Influencing factor: ___________________________________________________________ Rewrite question: ____________________________________________________________ ___________________________________________________________________________ b) A recent study shows that 45% of Canadians shop on the Internet. Amy writes this question for a survey: What do you buy online? Influencing factor: ___________________________________________________________ Rewrite question: ____________________________________________________________ ___________________________________________________________________________ 11.1 Factors Affecting Data Collection ● MHR 621 Name: _____________________________________________________ Date: ______________ Check Your Understanding Communicate the Ideas 1. Hakim says a survey can be biased without telling a lie. Write a survey question about the types of music people like. Make it biased, but with no lies in it. _______________________________________________________________________________ _______________________________________________________________________________ 2. A community uses a survey to decide whether to build a hockey arena or a swimming pool. Write the letter of the situation beside the influencing factor that matches it. a) The survey question is, “Do you want a fun-filled winter? Circle hockey as your choice!” bias ethics b) The survey is handed out at a swim meet. cost c) The community hires a survey company for $20 000. This cost is not in the budget. time/timing Practise 3. Each situation shows bias. Underline the part that needs to be changed to remove the bias. a) Ask hockey players if they are willing to pay higher registration fees for hockey. b) Ask new motorcyclists if helmets should be mandatory. c) Ask forestry workers if more money should be spent on fighting forest fires. 4. Underline the inappropriate part of each situation. a) A survey asks how much parents earn in 1 year. b) Only teachers are asked their opinion about a new school name. c) The Arts Council is surveyed about the importance of art classes in schools. 622 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ 5. Date: ______________ Rewrite each survey question so there are no influencing factors. a) b) Do you like to watch hockey, the only great sport? YES NO __________________________________________ Most people choose chocolate, but what is your favourite flavour of ice cream? __________________________________________ __________________________________________ __________________________________________ c) A recent survey shows that 42% of teens use the Internet to watch TV. What TV shows do you watch most often online? __________________________________________ __________________________________________ Apply 6. Write a survey question for each situation. Who would you ask to participate in the survey? a) Which sport teens like best Question : ____________________________________________________________________ _____________________________________________________________________________ Participants: __________________________________________________________________ b) If price or brand is more important when buying a cell phone Question : ____________________________________________________________________ _____________________________________________________________________________ Participants: __________________________________________________________________ c) Which Internet site people trust most to give them correct information Question : ____________________________________________________________________ _____________________________________________________________________________ Participants: __________________________________________________________________ 11.1 Factors Affecting Data Collection ● MHR 623 Name: _____________________________________________________ 7. Date: ______________ Rewrite each survey question so that it collects more helpful data. a) __________________________________________ If you are a juice drinker, would you consider switching to Crystal Juice? YES NO __________________________________________ __________________________________________ b) Which of the following cough medicines have you tried? __________________________________________ __________________________________________ __________________________________________ c) Are you satisfied with your Internet access? Circle one response. A Excellent B Good C Poor __________________________________________ __________________________________________ __________________________________________ Math Link One of the ways to save endangered species is to set aside land for them. You survey a sample of Canadians. Write 3 fair survey questions to find out who is in favour of creating National Parks for endangered species. Question #1: Find out if Canadians think the government should create National Parks. ___________________________________________________________________________________ Question #2: Find out if Canadians think the cost of the land is important to the decision. ___________________________________________________________________________________ Question #3: Find out if Canadians are worried about people who might be affected, such as those living on the land. ___________________________________________________________________________________ Test your questions with a classmate to see if they are clear and useful. 624 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ Date: ______________ 11.2 Warm Up 1. Sometimes we survey only a small number of people when we need information about the whole group. Give 1 reason why surveying everyone might be difficult. ________________________________________________________________________________ 2. Fill in the blanks with “more” or “less.” The people who are surveyed, the (more or less) accurate the results will be. 3. (more or less) Evaluate. a) 10% of a group of 350 10% of 350 = 0.1 × 350 b) 25% of a group of 788 To change a percent to a decimal, divide by 100. = 4. Calculate the percent of the population each situation represents. a) 12 out of a population of 240 people 12 = 240 ← decimal = ← percent This is % of the population. b) 90 out of a population of 450 people This is 5. % of the population. Starting at 1, list every seventh number between 1 and 100. ________________________________________________________________________________ 11.2 Warm Up ● MHR 625 Name: _____________________________________________________ Date: ______________ 11.2 Collecting Data Link the Ideas Working Example 1: Identify the Population population ● all of the individuals in the group being studied ● example: the population in an election is all the voters sample ● a group of individuals chosen from the population ● example: 100 voters chosen from each province or territory is a sample Identify the population for each situation. Would you survey a sample or the whole population? Why? a) A bike store owner wants to find out which brand of mountain bike her customers prefer. Solution ● ● The population is . (the store’s customers or high school students) Ask yourself, “Would it be possible to survey every customer?” Circle YES or NO. It depends on the size of the store. A small store might survey all of its customers. A large store would likely survey of its customers. (a sample or the whole population) It would be time-consuming and expensive for a large store to survey all the customers. b) The government of Canada wants to know how many high school students have Internet access. Solution ● Ask yourself, “Who does the government want to know about?” The population is in Canada. (high school students or people) ● Ask yourself, “Would it be possible to survey every high school student in the country?” Circle YES or NO. It would make sense to survey because it would take too much time to (a sample or the whole population) find all the high school students in Canada. 626 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ c) Date: ______________ A basketball coach needs to find out if the team wants to go to an out-of-town tournament. Solution ● Ask yourself, “Who does the coach need to ask?” The population is ● . Ask yourself, “Would it be possible to ask each person on the team?” Circle YES or NO. It would make sense to survey because the coach should get (a sample or the whole population) everyone’s input. For each situation, state ● the population ● whether you would survey the whole population or a sample ● your reason for surveying the population or a sample a) A store owner wants to find out if his customers are happy with the service. The population is . I would survey the because (whole population or sample) __________________________________________________________________________. b) The Royal Garden Restaurant wants to know which dish customers like best. The population is . I would survey the because (whole population or sample) __________________________________________________________________________. c) Stefan wants to find out if teachers in Canada prefer to wear glasses or contact lenses. The population is . I would survey the because (whole population or sample) __________________________________________________________________________. 11.2 Collecting Data ● MHR 627 Name: _____________________________________________________ Date: ______________ Working Example 2: Identify a Sample There are several types of samples. convenience sample ● choose individuals from the population who are easy to find or talk to voluntary response sample ● invite the whole population to participate Voluntary means you can choose whether to participate. random sample ● choose a specific number of individuals from the whole population ● random means that each individual has an equal chance of being chosen ● you can use data from a random sample to make predictions about the population ● there are 2 types of random samples: stratified sample ● First, divide the population into different groups. ● Then, choose the same percent of members from each group. systematic sample ● Choose individuals at fixed intervals (such as every fifth person) from an ordered list of the whole population. For each situation, describe how you could choose the sample. What type of sample would work best? a) A teacher wants to get feedback about a school dance from her class of 30 students. She plans to ask 5 students. Solution The teacher could put all the students’ names in a hat and choose 5 of them. This is a random sample. b) A company wants to see if its 3000 employees would use a fitness centre. It plans to survey 300 employees. Solution The company plans to survey out of 3000 employees. It could survey every tenth person on a list of employees. This is a systematic sample. 628 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ c) Date: ______________ A company is deciding whether to open a new store in Camrose, Alberta. The company surveys people in Camrose and 3 nearby towns. The table shows the population of each location. Town Population Camrose 16 000 Bashaw 825 Tofield 1 876 Daysland 876 Solution The company could survey 25% of the population in each This is a stratified sample. . d) A company mails a survey to all adults in a town. Everyone is asked to mail their responses back. Solution Since every voluntary response sample. is invited to participate in the survey, this is a This sample may not represent the population. Only those who are will respond. (interested or not interested ) e) A restaurant owner wants to know his customers’ favourite pizza topping. He surveys every customer who orders pizza between 5:00 p.m. and 10:00 p.m. Solution Is this a random sample? Circle YES or NO. Ask yourself, “Does every customer have a chance of being surveyed?” This is a convenience sample. Only customers who order pizza between those times are surveyed. 11.2 Collecting Data ● MHR 629 Name: _____________________________________________________ Date: ______________ 1. For each situation, what type of sample would you use? ● convenience ● voluntary ● random ● systematic ● stratified How would you choose the sample? a) A school librarian asks students which new fiction books she should order for the library. There are 424 students in the school. Type of sample: . Choose the students by ______________________________________________________ _________________________________________________________________________ b) A company plans to do a telephone survey to find out if people want a new art gallery. There are 800 000 people in the city. Type of sample: Choose the people by _______________________________________________________ _________________________________________________________________________ 2. Identify the type of sample in each case. a) A coach puts the names of all of the basketball players into a hat. Then, he draws 1 name for a free basketball. b) A company sends a questionnaire to every 9th person on an alphabetical list. c) The student council invites all students to suggest ideas for activities. d) The school principal asks each teacher to have 20% of their class answer a questionnaire. 630 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ Date: ______________ Check Your Understanding Communicate the Ideas 1. Kris decides to survey everyone in Canada to find out which bands are the most popular. a) Is this a survey of a sample or a population? Circle SAMPLE or POPULATION. b) Do you agree with his method? Circle YES or NO. Give 1 reason for your answer. ____________________________________________________________________________ ____________________________________________________________________________ 2. Kim and Scott want to know how many people took public transit to a concert. There are 18 000 people at the concert. Kim: I plan to ask the first 20 people who arrive. Scott: I plan to ask the first 200 people. a) Whose sample best represents the population? Circle KIM or SCOTT. Give 1 reason for your choice. ____________________________________________________________________________ ____________________________________________________________________________ b) What other type of sample would give more accurate results? Give 1 reason for your answer. correct ____________________________________________________________________________ ____________________________________________________________________________ 3. Describe the difference between surveying the population of British Columbia and surveying a sample of people who live there. _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ 11.2 Collecting Data ● MHR 631 Name: _____________________________________________________ Date: ______________ Practise 4. 5. Write the matching letter beside the type of sample that should be used for the situation. a) A large school surveys 20% of the students from each grade. random b) The school store asks the first 20 customers what type of juice they like the best. voluntary c) A company picks every 100th person in a phone book. convenience d) In a class of 40 students, each student is assigned a number. The teacher picks 5 numbers from a hat. stratified e) Students are asked to do an online survey if they wish. systematic Write the population in each situation. Would you survey the whole population or a sample of the population? Give 1 reason for your answer. a) The principal wants to know if teachers and students are in favour of school uniforms. Population: because _________________________________ I would survey (sample or population) _____________________________________________________________________________ b) An electronics store wants to know if its customers are happy with the repair department. Population: I would survey because _________________________________ _____________________________________________________________________________ c) The town wants to know if buses are needed for people with disabilities. Population: I would survey because _______________________________________________________ ______________________________________________________________ 632 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ Date: ______________ Apply 6. For each situation, would you survey the population or a sample? Give 1 reason for your answer. a) To determine the air quality in hospitals in Edmonton, Alberta: I would survey ________________________ because ________________________________ ____________________________________________________________________________. b) To find out the plans of grade 9 students after they graduate from high school: I would survey ________________________ because ________________________________ ____________________________________________________________________________. c) To test the quality of parachutes: I would survey ________________________ because ________________________________ ____________________________________________________________________________. d) To test the quality of bike tires: I would survey ________________________ because ________________________________ ____________________________________________________________________________. 7. Kristi wants to create a menu for a family picnic. Her family includes 20 adults, 8 teens, and 12 children. She only has time to talk to 10 people. How should she choose her sample? Explain. _______________________________________________________________________________ _______________________________________________________________________________ 8. Erin plans to survey her friends to determine the average number of children per household in Canada. a) Is this a random sample? Circle YES or NO. b) Give 1 reason for your answer. ____________________________________________________________________________ ____________________________________________________________________________ 11.2 Collecting Data ● MHR 633 Name: _____________________________________________________ 9. Jason wants to ask each student who enters the cafeteria the following question. Date: ______________ What is your favourite paint colour for the cafeteria walls? ________ a) What is the population? b) What is the sample? c) Will his results accurately represent the population? Circle YES or NO. Give 1 reason for your answer. _____________________________________________________________________________ Math Link Write a research question about an endangered animal. a) What endangered animal will you research? b) Find the size of the animal’s population before it was endangered. What is the population now? c) What is 1 reason for the decline of the population? _______________________________________________________________________________ _______________________________________________________________________________ d) Write a question that you can research about the endangered animal. _______________________________________ _______________________________________ Research Question: What are the population trends for beluga whales in Canada? _______________________________________ To answer your question, find data from studies and surveys that other people have done. e) What sampling method did researchers use to collect the data? Beluga whale, Somerset Island, Nunavut Give 1 reason for your answer. ______________________________________________________ _______________________________________________________________________________ 634 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ Date: ______________ 11.3 Warm Up 1. Explain what probability means by using a weather forecast. _______________________________________________________________________________ 2. Find the probability. Write your answer as a fraction, a decimal, and a percent. a) choosing a heart from a full deck of cards P(hearts) = b) spinning a B on the spinner number of favourable outcomes total number of outcomes A A B = 3. B C 52 = ← decimal (13 ÷ 52) = ← percent (multiply by 100) Find the mean, median, and mode of each set of data. a) 13, 10, 9, 13, 8 Mean = sum of items number of items Median: Write the numbers in order: 8, 9, b) 111, 132, 100, 123, 111, 100 Mean: Median: Add the two middle numbers and divide by 2. , 13, 13 The median is The mode is Mode: 11.3 Warm Up ● MHR 635 Name: _____________________________________________________ Date: ______________ 11.3 Probability in Society Link the Ideas Working Example 1: Use a Sample to Make a Prediction About the Population a) The grade 12 students in 5 of 7 high schools recorded their eye colour. A total of 2300 grade 12 students were surveyed. The table shows the results. Eye Colour Total Brown 1656 Blue 483 Green 115 Other 46 Predict how many of the 7200 students at a college will have brown eyes. Show your thinking. Solution Of the 2300 high school students surveyed, 1656 × 100 2300 = 0.72 × 100 % Step 2: Calculate 72% of 7200. 0.72 × 7200 = Step 3: Write a prediction statement. Approximately 636 students at the college will have brown eyes. MHR ● Chapter 11: Data Analysis To predict is to tell what might happen. students have brown eyes. Step 1: Find the percent of students who have brown eyes: = Literacy Link Name: _____________________________________________________ Date: ______________ b) Is your prediction reasonable? Explain why or why not. Solution No, not necessarily. There is an assumption that the high school sample represents the college population. The sample represents the grade Literacy Link An assumption is something taken for granted, as if it were true. population. The sample may not represent the college student population. Students may come from other high schools, provinces, territories, or countries. So, the sample is a biased sample. The prediction may be for the college population. (valid or not valid ) biased sample ● does not represent the population ● can make survey results inaccurate or not valid c) Rewrite a more accurate prediction statement. Solution If the student population in the high schools and college are , (different or similar) approximately 5200 college students have A total of 2300 grade 12 students were surveyed. Predict how many college students have blue eyes. Step 1: Find the percent of students who have blue eyes. eyes. Eye Colour Total Brown 1656 Blue 483 Green 115 Other 46 Step 2: Calculate the number of 7200 college students who have blue eyes. Step 3: Write a prediction statement. _____________________________________________________________________________ 11.3 Probability in Society ● MHR 637 Name: _____________________________________________________ Date: ______________ Working Example 2: Avoid Making a False Prediction Mr. Krutz gave an assignment worth 30 marks. After marking the first 5 papers, he was worried that the students did not understand the assignment. He predicted that most of the students would not do well. a) Use Mr. Krutz’s sample of marks to predict the class’s average mark. Write the average mark as a percent. Solution Use the measures of central tendency. Mean = = mean, median, and mode sum of items number of items 20 + 15 + 18 + = + 5 5 = The mean is . The median is the middle number. First, write the numbers in order: 15, 18, 18, 19, . The median is The mode is the number that appears the most often. The mode is . . The mean, median, and mode for the sample are 18. Average mark = 18 × 100 30 = 0.6 × 100 = % Based on the sample statistics, I predict the average mark as a percent is 638 MHR ● Chapter 11: Data Analysis . Name: _____________________________________________________ Date: ______________ b) The scores for all 30 students in the class are: 20 15 18 19 18 16 17 23 24 30 22 24 21 20 24 25 19 24 15 28 27 28 22 24 19 13 28 22 24 20 Why did Mr. Krutz’s sample lead him to make a false prediction? Literacy Link A false prediction is an incorrect prediction. Solution The mean, median, and mode for all the marks are ● mean = 21.6333… ● median = 22 Which mark appears ● the most often? mode = Mr. Krutz assumed that the sample of the first This is FALSE. papers was representative of the whole class. The mean score in the sample is 60%. The mean score in the class is approximately 21.63 × 100 30 = % The mode written as a percent is 24 × 100 30 = 0.8 × 100 = % Mr. Krutz may have used too small of a sample to make his prediction. The sample represent the population. (does or does not) 11.3 Probability in Society ● MHR 639 Name: _____________________________________________________ Look at Mr. Krutz’s students’ marks. 20 15 18 19 18 16 17 23 24 30 22 24 21 20 24 25 19 24 15 28 27 28 22 24 19 13 28 22 24 20 Date: ______________ last 5 papers a) Predict the average mark if Mr. Krutz had marked the last 5 papers first. Use the measures of central tendency. Mean = sum of items number of items The mean is . Median: Write the numbers in order: The median is The mode is . . Average mark: Prediction: _________________________________________________________________ b) Do these marks give a more reasonable prediction of the class average? Circle YES or NO. Give 1 reason for your answer. __________________________________________________________________________ 640 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ Date: ______________ Working Example 3: Make a Decision Based on Probability A youth association surveys 400 members about their favourite activity. There are 100 members in each of 4 different groups. The table shows the survey results. Group Swimming Rock Climbing Watching Movies Bowling Total Red 14 9 40 37 100 Blue 11 19 59 11 100 Green 27 12 57 4 100 Yellow 13 24 44 19 100 a) What is the theoretical probability that a member of any group will choose swimming? Based on your answer, predict how many of the 400 members will choose swimming. Solution Literacy Link The members have an equal chance of choosing any 1 of the 4 activities. P(swimming) = number of favourable outcomes total number of outcomes = 1 or 4 theoretical probability The chance of an event happening. Theoretical probability # of favourable outcomes = total # of outcomes % The theoretical probability that a member of any group will choose swimming is Predict how many of the 400 members will choose swimming. . 1 × 400 4 400 = 4 = I predict that members will choose swimming. b) What assumptions did you make? Solution ● Every activity has an ● (equal or unequal) Members have the same interest in each activity. chance of being selected. 11.3 Probability in Society ● MHR 641 Name: _____________________________________________________ Date: ______________ Use the results in the table to predict the probability that a member will choose swimming. c) Group Swimming Rock Climbing Watching Movies Bowling Total Red 14 9 40 37 100 Blue 11 19 59 11 100 Green 27 12 57 4 100 Yellow 13 24 44 19 100 Solution Literacy Link Use experimental probability to help make the prediction. experimental probability The chance of an event happening based on the results of an experiment. number of favourable outcomes total number of outcomes 14 + 11 + 27 + 13 = 400 P(swimming) = = Write Experimental probability # of favourable outcomes = total # of outcomes 400 65 as a percent. 400 65 × 100 400 = 0.1625 × 100 = % The experimental probability that a member will choose swimming is %. d) Compare your answers for parts a) and c). Explain any differences. Solution 25% 16.25% (> or <) The < means less than > means greater than probability is greater than the (theoretical or experimental) probability. The (theoretical or experimental) probability shows a truer picture of the youths’ interests. (theoretical or experimental) 642 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ Group Red Blue Green Yellow Date: ______________ Swimming Rock Climbing Watching Movies Bowling Total 14 11 27 13 9 19 12 24 40 59 57 44 37 11 4 19 100 100 100 100 a) What is the experimental probability that a member will choose each of the following? Watching Movies: Bowling: b) Pretend you are a youth coordinator planning the activities. How would you figure out the members’ favourite activity? Give 1 reason for your answer. ___________________________________________________________________________ ___________________________________________________________________________ Check Your Understanding Communicate the Ideas 1. Look at the cartoon. Explain how this sample could result in a false prediction. _______________________________________________________________________________ _______________________________________________________________________________ 11.3 Probability in Society ● MHR 643 Name: _____________________________________________________ 2. Date: ______________ You need to choose what flavours of ice cream to sell at a soccer tournament. How could you use experimental probability and theoretical probability to help choose? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ Practise 3. A light bulb factory samples light bulbs as they come off the assembly line. A random sample shows that 1 bulb out of every 20 does not work. The manager predicts that 50 bulbs out of 1000 will not work. a) How did the manager make his prediction? 1 × 20 1 ÷ 20 = ? = × = bulbs b) What assumption did the manager make? ____________________________________________________________________________ ____________________________________________________________________________ 4. A toothpick factory samples every 100th toothpick for damage. The sample shows a 1% probability of damage. How many toothpicks out of 2 million toothpicks do you predict will be damaged? 1 × 100 = 644 toothpicks MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ 5. Date: ______________ A movie rental company has 5 types of movies: drama, comedy, horror, action, and science fiction. a) What is the theoretical probability that a person will choose a comedy? P(comedy) = number of favourable outcomes number of choices b) What assumptions did you make? ____________________________________________________________________________ c) The table shows the movie preferences from a random survey of 50 customers. Predict the probability that a customer will choose a comedy movie. P(comedy) = number of favourable outcomes number of responses Movie Type Responses Drama Comedy Horror Action Science fiction 15 5 12 16 2 The probability that a customer will choose a comedy movie is out of 50 or %. d) Give 1 reason why the theoretical probability is different from the experimental probability. ____________________________________________________________________________ ____________________________________________________________________________ 11.3 Probability in Society ● MHR 645 Name: _____________________________________________________ Date: ______________ Apply 6. Jack wants to know the weekly part-time earnings of grade 9 students. He randomly surveys 5 grade 9 students. The results are: $75, $125, $25, $250, and $25. a) Is this a biased sample? Circle YES or NO. Give 1 reason for your answer. ____________________________________________________________________________ b) Jack says that grade 9 students who work part-time earn an average of $100 per week. Do you agree? Explain and show your thinking. ____________________________________________________________________________ 7. Miya received these scores from 10 judges in a skating competition. The scores are out of 10. Judge Score 1 8.5 2 6 3 6.5 4 6.5 5 6.5 a) Use all 10 judges’ scores to find Miya’s mean score. 6 7 7 6 8 6.5 9 4.5 10 7 b) Use the first 3 judges’ scores as a sample. Calculate the mean. c) Use the last 3 judges’ scores as a sample. Calculate the mean. d) Compare the mean from each sample to the mean for all judges. Are the samples good predictors for Miya’s overall score? Circle YES or NO. Give 1 reason for your answer. ____________________________________________________________________________ ____________________________________________________________________________ 646 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ Date: ______________ Math Link Use data from studies and surveys for your research project. Use the library or the Internet. a) Use your research question from Math Link 11.2 on page 634. What data will you look for? _______________________________________________________________________________ _______________________________________________________________________________ Where will you look? _______________________________________________________________________________ _______________________________________________________________________________ b) Answer the following questions for 2 studies or surveys related to your question. • Did the sampling method involve the whole population or a sample? Describe. Study 1: Study 2: ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ • How was the data collected? Describe. Study 1: Study 2: ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ 11.3 Math Link ● MHR 647 Name: _____________________________________________________ Date: ______________ • What were the results for each method? Study 1: Study 2: ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ • What assumptions were made? Study 1: Study 2: ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ • How accurate are any predictions made about the population? Study 1: Study 2: ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ • Where did you find each study or survey? Who wrote each study? 648 Study 1: Study 2: ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ ____________________________________ MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ Date: ______________ 11.4 Warm Up 1. What is the difference between surveying a population and surveying a sample of a population? A sample is a 2. of a population. Give an example or a description of each of the following: a) biased sample _____________________________________________________________________________ _____________________________________________________________________________ b) convenience sample _____________________________________________________________________________ _____________________________________________________________________________ c) random sample _____________________________________________________________________________ _____________________________________________________________________________ d) voluntary response sample _____________________________________________________________________________ _____________________________________________________________________________ 3. a) How could the fisheries department estimate the average number of sea lice on salmon without looking at every salmon caught? The fisheries department could take a lice on them. of salmon and count the sea They could then find the number of sea lice and assume the same is true for the whole . b) If there are 90 sea lice on 30 salmon, what is the average number of sea lice per salmon? Sentence: _______________________________________________________________________ 11.4 Warm Up ● MHR 649 Name: _____________________________________________________ Date: ______________ 11.4 Developing and Implementing a Project Plan Step 1: Finalize your research project. 1. The animal you are studying is 2. List 2 things you know about the animal: . ________________________________________________________________________________ ________________________________________________________________________________ 3. Write the population information you found in your research. ________________________________________________________________________________ ________________________________________________________________________________ 4. Explain 1 possible reason why the animal is endangered. ________________________________________________________________________________ ________________________________________________________________________________ 5. List where you got your information. ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ 6. Describe how the scientists collected the data. How did they use the data to make a hypothesis about the health of the animal population? Literacy Link A hypothesis is a statement that guides an experiment. ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ 650 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ Date: ______________ Step 2: Create a rubric for your research project. The expectations are listed in column 1. For each expectation, write an explanation for each of the 4 levels of performance. • • • • Level 1 is for work that does not meet the expectation. Level 2 is for work that meets the minimum expectation. Level 3 is for work that meets the expectation. Level 4 is for work that is better than the expectation. The first row is done for you. Expectation Planning • question and hypothesis • description of population Level 1 Level 2 Level 3 Level 4 • not clear • fairly clear • mostly clear • very clear • limited or not • some • good enough • detailed complete description description description Performing • research and data collection Recording • display of data Analysing • analysis • conclusion(s) Presenting • project plan and evaluation of results 11.4 Developing and Implementing a Project Plan ● MHR 651 Name: _____________________________________________________ Date: ______________ Step 3: Develop the project plan. a) Describe how you will organize and display your data. Will you use a table? What type of graph will you use? ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ b) Describe how you analysed the data from the studies. • What assumptions did you make? ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ • If you made any predictions, how close were they? ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ c) Describe how you will present your findings. Will you make a poster, do an oral or written presentation, use technology, or use a combination of methods? ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ ________________________________________________________________________________ 652 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ Date: ______________ Step 4: Complete the project. a) Display the data on a graph. b) Make a prediction from your data. ________________________________________________________________________________ ________________________________________________________________________________ c) Answer the following questions to evaluate your results. • Do the data answer your question from Math Link 11.2? Circle YES or NO. • Do you need to do more research? Circle YES or NO. • Are the data biased? Circle YES or NO. Give 1 reason for your answer. ________________________________________________________________________________ • Write 2 questions you could ask as a result of your research. ________________________________________________________________________________ ________________________________________________________________________________ • What other sampling methods could the researchers have used? ________________________________________________________________________________ ________________________________________________________________________________ 11.4 Developing and Implementing a Project Plan ● MHR 653 Name: _____________________________________________________ Date: ______________ Step 5: Present your findings in a format of your choice. You must include a title a research question a description of the population for the studies researched, – the sampling methods – the data collection methods – the results and conclusions your display of the data your answer to research question your evaluation of your research results a bibliography of all sources Math Link: Wrap It Up! Step 6: a) Describe 1 good thing you learned from the research about your animal. _______________________________________________________________________________ b) What is 1 thing that makes studying your animal’s whole population challenging? _______________________________________________________________________________ c) What 1 thing could be done to increase the probability of your animal’s survival? _______________________________________________________________________________ d) Does your research suggest your animal will survive without the help of people? How do you know? _______________________________________________________________________________ e) Write 1 sentence that describes what you have learned from your research. _______________________________________________________________________________ f) What should scientists do next to find out more about your animal’s survival? _______________________________________________________________________________ g) What is the main type of sampling used to study your animal? What other methods could be used? _______________________________________________________________________________ 654 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ Date: ______________ Graphic Organizer Define each term and give an example. Non-random convenience: Random stratified: voluntary: systematic: Sample Data Analysis Population Influencing Factors Examples: Definition: Example: Graphic Organizer ● MHR 655 Name: _____________________________________________________ Date: ______________ Chapter 11 Review Key Words For #1 to #9, write the number that matches the description. 1. an example is every 10th person in a line-up convenience sample 2. bias and cost are examples of these population 3. an example is polling 2 students out of 100 about who will win an election influencing factors sample 4. an example is the first 30 people entering the gates at a football game 5. any group of individuals selected from a population biased sample voluntary response sample random sample 6. a specific number of people selected from a population systematic sample 7. the whole group of people being studied stratified sample 8. an example is dividing the population into males and females and then randomly selecting a proportional number from each group 9. an example is a population invited to call in to a radio talk show 11.1 Factors Affecting Data Collection, pages 618–624 10. Name 1 influencing factor for each situation. Influencing factors: • bias • use of language • ethics • cost • time and timing • privacy • cultural sensitivity a) Ask the first 40 people entering a park office if they think parks are worth the cost. _____________________________________________________________________________ b) Ask 10 randomly chosen grade 8 students if the grade 12 students should have a special dance. _____________________________________________________________________________ c) Ask 15 juice drinkers if they support replacing juice in the vending machine with bottled water. _____________________________________________________________________________ 656 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ Date: ______________ 11. Write 1 influencing factor that may affect data collection. Then, rewrite the survey question. a) You look like a good citizen. Do you support more money for hospitals? Influencing factor: Rewrite question: ______________________________________________________________ _____________________________________________________________________________ b) Everybody loves The Rockets. Who is your favourite rock group? Influencing factor: Rewrite question: ______________________________________________________________ _____________________________________________________________________________ c) Do you prefer ice hockey or cake after school? Influencing factor: Rewrite question: ______________________________________________________________ _____________________________________________________________________________ 11.2 Collecting Data, pages 626–634 12. Identify the population for each situation. Then, describe how you would select a sample for each. a) the spending habits of teens in Canada Population: I would select a sample by _______________________________________________________. b) the popularity of different kinds of music in your school Population: I would select a sample by _______________________________________________________. c) the cost of gasoline in your community Population: I would select a sample by _______________________________________________________. Chapter 11 Review ● MHR 657 Name: _____________________________________________________ Date: ______________ 13. For each situation, identify the type of sample. Identify any bias in each sample. a) Survey the first 20 shoppers to enter the north entrance of a mall. Sample type: There could be bias because _____________________________________ Types of samples: • convenience • voluntary • random • stratified • systematic ____________________________________________________________. b) Divide youth conference delegates into groups according to the western province or territory where they live. Then, randomly select 20 youths from each group. Sample type: There could be bias because _____________________________________________________. c) The area supervisor for a fast-food chain selects employees at 1 store location. Sample type: There could be bias because _____________________________________________________. ____________________________________________________________________________ 14. What type of sample do you suggest for each situation? Give 1 reason for your choice. a) a survey of customers to find out their favourite sundae topping Type: Reason: ______________________________________________________________________ _____________________________________________________________________________ b) a survey of doctors, nurses, and hospital administrators to find out if the hospital needs to add more patient rooms Type: Reason: ______________________________________________________________________ _____________________________________________________________________________ 658 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ Date: ______________ 11.3 Probability in Society, pages 636–648 15. A town of 4000 people is electing a mayor. A reporter asked 40 people who they voted for. He found that 50% chose Candidate A, 20% chose Candidate B, and the rest chose Candidate C. a) How many people surveyed chose Candidate B? Sentence: ____________________________________________________________________ b) What is the theoretical probability that a voter will choose Candidate A? P (Candidate A) = = number of Candidate A’s total number of candidates 1 What assumption did you make? __________________________________________________ Use the survey results. c) Compare the experimental and theoretical probability of Candidate A winning. _____________________________________________________________________________ d) The reporter predicts that Candidate A will win the election. Do you agree with his prediction? Circle YES or NO. Give 1 reason for your answer. _____________________________________________________________________________ 16. Nancy is running for treasurer on student council. There are 28 students in her class. Twenty classmates say they will vote for her. Nancy predicts that 75% of the 328 grade 9 students will vote for her. a) Is her prediction reasonable? Show your thinking. Change 20 to a percent. 28 Sentence: ____________________________________________________________________ b) Write a prediction that would be more accurate. ____________________________________________________________________________ ____________________________________________________________________________ Chapter 11 Review ● MHR 659 Name: _____________________________________________________ Date: ______________ Key Word Builder Fill in the blanks with the correct key word. Then, find each word in the word search. BIASED CONVENIENCE POPULATION RANDOM SAMPLE STRATIFIED SYSTEMATIC VOLUNTARY 1. A of the population in a federal election might be 100 individuals from each province or territory. 2. A whole population. 3. A sample means dividing the whole population into distinct groups, then choosing the same percent of members from each group. 4. A company interviews every 10th person on the payroll list. This is a sample. 5. The 6. A sample is 7. The research company invites all the residents of a town to participate in a survey. sample means choosing a certain number of individuals from the in a federal election is all eligible voters. when it does not represent the whole population. This is a 8. response sample. Rhett only surveyed students who were his friends because they were easy to access. This is an example of a S T N G R E E F E Y X O L D F 660 C Y Y Q X E A M C Q Q Q C R E sample. W B I A S E D N N B V X T B S C Y D H M E R G E C N M Q G T L I R J K I S A I Y J Q V J R MHR ● Chapter 11: Data Analysis U S T R N Y X E N P W O R V A R A K A L N V W E D L N Y F T W M I X M J W Q V U O Z R D I R P M Z C E F D N G K M V V F Z L T Z I B T T O H C Y P G I Y E L Y S V A S C I W Y Z T E U Z R G H R T X Y X U N I K D X V D A Y T L X Y S M Q V U I N O I T A L U P O P N M A L Z J X U F K K V Z K J V F Q E Y Name: _____________________________________________________ Date: ______________ Chapter 11 Practice Test For #1 to #4, choose the best answer. 1. A company displayed 2 sports shirts at a school with 500 students. The students were asked the following question. Over 78% of students at Central High will buy Shirt B. Which one of these two sports shirts would you buy? A: $35.99 B: $44.99 What influencing factor might affect the data being collected? 2. 3. 4. A bias B timing C ethics D cultural sensitivity Diana wants to survey grade 9 students about their favourite flavour of soft drink. Which question is most appropriate? A Is cola your favourite type of soft drink? B Do you like soft drinks? C What is your favourite flavour of soft drink? D What brand of soft drink do you like? An eco-tourism company is researching how to expand its tours. It divides the western provinces into 8 areas. Then, it surveys 10% of the population in each area. Which sampling method is this? A convenience sample B stratified sample C systematic sample D voluntary response sample A business sends questionnaires to 50% of its employees randomly selected from a list. Which sampling method is this? A convenience sample B stratified sample C systematic sample D voluntary response sample Complete the statements in #5 to #7. 5. A small group that represents a population is a . 6. Choosing members of the population at fixed intervals from a membership list describes a . 7. A Web site that asks browsers to fill out an online survey is using a . Chapter 11 Practice Test ● MHR 661 Name: _____________________________________________________ Date: ______________ Short Answer 8. Cheyenne surveys students in her high school about types of music for a school dance. They can choose rap, alternative, rock, or country. a) What is the population for this study? The population is . b) Write a clear survey question that is free from influencing factors. _____________________________________________________________________________ _____________________________________________________________________________ c) Describe a sampling method Cheyenne could use. _____________________________________________________________________________ _____________________________________________________________________________ 9. On an assembly line for cell phones, a random sample shows 3% are defective. a) How many do you predict would be defective if 3248 were made? Sentence: _____________________________________________________________________ b) Write 1 assumption you made in your prediction. _____________________________________________________________________________ _____________________________________________________________________________ 662 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ Date: ______________ Challenge Global Warming Tornados, floods, droughts, tsunamis, killer heat waves, and other extreme weather events often make the news. Many climate scientists link extreme weather events to global warming. You be the climate scientist. Collect and analyse weather data to determine if there is a warming trend in a location of your choice. a) Use the Internet or the library to find temperature information for your location. Find the mean annual temperatures for each year for the last 10 years. Location: Year Mean Annual Temperature (°C) b) Graph your data. y Mean Annual Temperature (ºC) 1. x Year 2. a) Is there a warming trend in the area you analysed? Circle YES or NO. Give 1 reason for your answer. _____________________________________________________________________________ b) Do your findings support global warming? Circle YES or NO. Give 1 reason for your answer. _____________________________________________________________________________ Challenge ● MHR 663 Name: _____________________________________________________ Date: ______________ Chapters 8–11 Review Chapter 8 Solving Linear Equations 1. Solve each equation. Write your answers in lowest terms. a) 8x = 2 5 8x ÷ b) = 2 ÷ 5 x= 2 × 5 x 5 = 6 9 × x 5 = × 6 9 x= 2. A triangle has an area of 10.54 m2 and a base length of 6.2 m. What is the height of the triangle? A= b×h 2 h b = 6.2 m Sentence: _______________________________________________________________________ 3. Bruno bought 4 boxes of granola. He received $6.04 in change from a $20.00 bill. How much did he pay for each box of granola? Let b = cost of 1 box of granola. Cost of 4 boxes of granola + 6.04 = 20.00 Equation: Solve: Sentence: ________________________________________________________________________ 664 MHR ● Chapter 11: Data Analysis Name: _____________________________________________________ 4. Date: ______________ Two electricians each charge a fee for a service call, plus an hourly rate for their work. Theo charges $49.95 plus $40.00 per hour. Vita charges $69.95 plus $32.00 per hour. For what length of service call do Theo and Vita charge the same amount? Let x = the number of hours of service. Theo Vita Initial Fee Hourly Rate Total Charge for Service Theo’s total charge for service = Vita’s total charge for service Sentence: ________________________________________________________________________ 5. The equilateral triangle and the square have equal perimeters. What is the side length of the square? Perimeter of triangle = perimeter of square 3x + 4 ( The value of x is + )= ( + 2x + 5 ) . Find the side length of the square. 2x + 5 Sentence: ________________________________________________________________________ Chapters 8–11 Review ● MHR 665 Name: _____________________________________________________ Date: ______________ Chapter 9 Linear Inequalities 6. Write the inequalities using algebra. a) 14 16 18 20 b) -7 -6 -5 and x (≤ or ≥) (16 or 17 or 18) 7. Show each inequality using a graph. a) x < – 6 b) x ≥ 2.4 -10-9-8 -7 -6 -5 -4 -3 -2 -1 0 1 8. 1 2 3 Write an inequality to show each politician’s election promise. a) We will start at least 8 new highway projects. Variable: Let h = the number of highway projects. Inequality: h 8 (≤ or ≥) b) There will be a budget surplus of over $1.3 million this year. Surplus means extra money. Variable: _____________________________________________________________________ Inequality: 9. Solve each inequality. a) x + 6.2 < 15 b) –25x < 125 When multiplying or dividing by a negative number, reverse the inequality symbol. c) 666 x ≥ –10 5 MHR ● Chapter 11: Data Analysis d) 20 – x ≤ 8 Name: _____________________________________________________ Date: ______________ 10. Solve the inequality. Then, verify the solution. 4x + 17 ≥ 35 Check a value for equal: Left Side Subtract 17. 4x + 17 Right Side 35 Divide by 4. Check a value for greater than: 11. Lori is renting a climbing wall. The rental charge is $145/h. She cannot spend more than $800. For how many hours can Lori rent the wall and still stay within her budget? a) Write an inequality to model this problem. Variable: Let h = __________________________________________. Inequality: b) Solve the inequality and write a sentence to explain the situation. Sentence: _____________________________________________________________________ Chapters 8–11 Review ● MHR 667 Name: _____________________________________________________ Date: ______________ Chapter 10 Circle Geometry 12. a) What is the measure of ∠DEB? D ∠DEB is a(n) angle. ∠DEB = ∠DAB because they share the same So, ∠DEB = . C A 47° B °. E b) What is the measure of ∠DCB? Justify your answer. ∠DCB is a angle. ∠DCB = ×∠ = × = ° So, ∠DCB is ° °. 13. CD bisects chord AB. radius = 7 cm chord AB = 9 cm What is the length of CE? Round your answer to the nearest tenth. cm A Label the diagram with the measurements you know. Chord AB = , so AE = 2 2 Formula → CE + 2 = Substitute → Solve → The length of CE is 668 cm. MHR ● Chapter 11: Data Analysis C cm E D B Name: _____________________________________________________ Date: ______________ E 14. Radius CG is perpendicular to chord EF. Chord EF is 7 mm from C. radius = 25 mm What is the length of chord EF? 7 mm C Draw a line from C to F. Write the measurements on the diagram. H G F Formula → Substitute → Solve → FH is mm. EF = FH × = Influencing factors: ● bias ● use of language ● ethics ● cost ● time and timing ● privacy ● cultural sensitivity × = The length of chord EF is mm. Chapter 11 Data Analysis 15. For each survey question, write 1 influencing factor. Then, rewrite the question to improve it. a) Do you like to play cards, the greatest indoor game? YES NO b) The student council wants to know how cheap you are! Do you want a real band ($10 per ticket), or just a DJ ($5 per ticket) at the dance? Influencing factor: Influencing factor: Rewrite question: Rewrite question: Chapters 8–11 Review ● MHR 669 Name: _____________________________________________________ Date: ______________ 16. You decide to survey students about their online activities. a) What is the population? b) List 2 different sampling methods you could use. and 17. A recreation centre offers lessons in 5 types of activities: soccer, basketball, swimming, lacrosse, and figure skating. a) What is the theoretical probability that a person will choose swimming? P(swimming) = number of favourable outcomes total number of outcomes = b) What assumptions did you make? _____________________________________________________________________________ _____________________________________________________________________________ c) The table shows the activity preferences from a random survey of 50 customers. Predict the probability that a customer will choose swimming. P(swimming) = number of favourable outcomes total number of outcomes Activity Soccer Basketball Swimming Lacrosse Figure Skating Number of Votes 15 5 12 16 2 = = ← decimal = ← percent The probability that a customer will choose a swimming is out of 50 or %. d) Give 1 reason why the theoretical probability is different from the experimental probability. ____________________________________________________________________________ ____________________________________________________________________________ 670 MHR ● Chapter 11: Data Analysis Answers Get Ready, pages 614–615 Apply 1. a) mean = 7; median = 6; modes = 8 and 15 b) mean = 4.5; median = 4.4; no mode 6. Answers may vary. Examples: a) Which sport do you like best? Participants: people between the ages of 13 and 19 b) What is most important to your choice of cell phone: price or brand? Participants: people about to purchase a cell phone c) Which Internet site do you trust to give you accurate information? Participants: people who use the Internet to find information. 2. a) 6 b) 24 3. a) A b) 17 L Math Link 1. 7. Answers may vary. Examples: a) Do you drink juice? YES or NO. If yes, would you switch to Crystal Juice? b) Do you use cough medicines? YES or NO. If yes, which brands do you use? c) Do you have Internet access? YES or NO. If yes, how satisfied are you with the level of service you get? Population Approximate Total Park Count (2007 Fall Count) 700 600 500 400 300 200 100 0 Math Link Answers may vary. Examples: Plains Bison Wood Bison Elk Moose Question #1: Do you think the Federal Government should create National Parks? YES or NO. Question #2: Does the cost of the land matter to you? YES or NO. Question #3: Do you believe that people living on future National Parks should be consulted? YES or NO. Deer Ungulate Approximate Total Park Count (2007 Fall Count) 11.2 Warm Up, page 625 1. Answers may vary. Examples: Since there are so many people who live in a country, it might be difficult or expensive to survey all of them. Deer Moose 2. more; more or less; less 3. a) 35 b) 197 Elk 4. a) 5% b) 20% Wood bison Plains bison = 100 deer = 100 moose = 100 elk = 100 wood bison = 100 plains bison 5. 1, 8, 15, 22, 29, 36, 43, 50, 57, 64, 71, 78, 85, 92, 99 11.2 Collecting Data, pages 626–634 Working Example 1: Show You Know 2. Elk 3. a) 3 Elk b) 36% 11.1 Warm Up, page 617 1. a) approximately 98 books b) Adventure books 2. a) 66.7% b) NO. The circle graph shows 100% of the books they signed out. 3. 50 4. 10% of the school was surveyed. 11.1 Factors Affecting Data Collection, pages 618–624 Working Example 1: Show You Know a) NO. Answers may vary. Examples: Asking only grade 12 students is not fair. Asking only 10 students is not a large enough sample. b) The survey could be improved by asking more students in a variety of grades. Working Example 2: Show You Know a) bias; Do you think the hunting of polar bears should be stopped? b) use of language; Do you shop online? YES or NO. If yes, what kinds of products or services do you buy? Communicate the Ideas 1. Answers may vary. Example: Most students prefer rock and roll to jazz. Would you prefer the school radio station to play more rock and roll or more jazz? 2. a) bias b) time/timing c) cost Practise 3. a) Ask hockey players if they are willing to pay higher registration fees for hockey. b) Ask new motorcyclists if helmets should be mandatory. c) Ask forestry workers if more money should be spent on fighting forest fires. 4. a) A survey asks how much parents earn in 1 year. b) Only teachers are asked their opinion about a new school name. c) The Arts Council was surveyed about the importance of art classes in schools. 5. Answers may vary. Examples: a) Do you like to watch hockey? b) What is your favourite flavour of ice cream? c) Do you watch TV online? YES or NO. If yes, what TV programs do you watch most online? Answers may vary. Examples: a) the store’s customers; sample; it would be difficult to get every customer to participate b) the restaurant’s customers; sample; all customers might not want to participate c) teachers in Canada who wear glasses or contacts; sample; it would be too expensive and difficult to survey every teacher in the country. Working Example 2: Show You Know 1. Answers may vary. Examples: a) voluntary response; use a suggestion box in the library b) systematic; sample every 1000th person in phone book. 2. a) random b) systematic c) voluntary response d) stratified Communicate the Ideas 1. a) POPULATION b) NO; it is too expensive and difficult to survey everyone. 2. a) SCOTT; the more people surveyed, the more accurate the response will be. b) systematic sample; it would survey people who arrived late, perhaps because they took their own vehicles rather than public transit. 3. Surveying the population means surveying every person in BC. A sample is only a part of the whole population. Practise 4. a) stratified b) convenience c) systematic d) random e) voluntary 5. a) teachers and students of the school; sample; it is less timeconsuming and expensive. b) customers who use the repair department; sample; all customers might not want to be surveyed. c) people with disabilities; sample; it would be difficult to find everyone with a disability to survey. Apply Answers may vary. Examples: 6. a) population; there are not that many hospitals, so it is possible to survey the population. b) sample; it would be hard to survey grade 9 students. c) population; all parachutes must be safe. d) sample; it would be too expensive to test all tires. 7. Kristi could draw the names of 5 adults, 2 children, and 3 teens out of a hat. This way, she would talk to 25% of each group. Answers ● MHR 671 8. a) NO b) Erin’s friends are a specific group not a random selection. 9. a) Students who use the cafeteria. b) convenience c) YES. He is asking the people who use the cafeteria. 2. It is one of the most endangered species in the world; there are only 25 living in the wild. 3. There were 300 in the mid-1980s, then 75 in 2001. Math Link 4. Their habitat is disappearing. Answers will vary. Examples: a) Vancouver Island marmot b) over 300; less than 75 in 2001 c) Clearcut logging affected their habitat. d) What can be done to save the species? e) Random sampling was used because they had to catch the marmots using traps. They could not control which ones they captured. 5. Internet sites and library books. 11.3 Warm Up, page 635 6. Scientists use systematic samples. Since they keep finding fewer and fewer marmots, they know the population is in decline. Step 2: 1. Answers may vary. Example: A weather forecast gives the probability of precipitation. A high probability means it probably will rain or snow, but doesn’t always mean it will for sure. 13 2 2. a) ; 0.25; 25% b) ; 0.4; 40% 52 5 3. a) mean = 10.6; median = 10; mode = 13 b) mean = 112.8; median = 111; mode = 111 and 100 Expectation Planning 11.3 Probability in Society, pages 636–648 Performing Working Example 1: Show You Know • research and data collection Step 1: 21% Step 2: 1512 Step 3: Approximately 1512 college students will have blue eyes. Working Example 2: Show You Know a) mean = 21.4; median = 22; no mode. Prediction: The average mark is 21.4 or 71.3%. b) YES; The last numbers contain more 20s, which is 30 common in the class, but not common in the first 5 numbers. Apply 6. a) YES; the sample is too small. b) No; since the sample is biased, it could be incorrect. 7. a) 6.5 b) 7 c) 6 d) Answers may vary. Example: YES; they are close to the actual mean. Math Link a) Answers may vary. Example: I will look for experiments about the effect of reintroducing marmots into the wild. I will look at the marmot research centre online. b) Answers will vary. 11.4 Warm Up, page 649 1. part 2. Answers may vary. Examples: a) Asking only teachers about changing the school hours. b) Asking only the people entering a mall about the cleanliness of the mall. c) Picking names from a hat. d) Sending a questionnaire in the mail. 3. a) sample; average; population b) The average number of sea lice on 90 salmon is 3. 11.4 Developing and Implementing a Project Plan, pages 650–654 Answers will vary. Examples: Step 1: 1. The Vancouver Island marmot • no research or incomplete or inappropriate data collection • current • excellent • some research research research and data and data and current collection and data from a but may be sufficient to variety of too little, or make good too old conclusions sources • data is in • data is • data is not • data is in displayed; table or both table displayed can’t be graph form and graph clearly in a understood only and is form and is variety of fairly easy easy to easy-toto understand understand understand formats Recording • display of data • analysis is • analysis • unclear or • analysis incorrect can be clear and and conclusions understood supports conclusion • conclusion(s) and the correct are very conclusion conclusion clear and makes some entirely sense correct Presenting • project plan and evaluation of results • presentation is unclear or incomplete • presentation is fairly clear and matches the evaluation of results MHR ● Chapter 11: Data Analysis • presentation not only explains the project results but is highly educational as well b) I assumed that no marmots had been bred in captivity. My prediction was that there would be fewer left. c) I will use a PowerPoint presentation to show pictures of the marmots, their habitat, the effects of clear-cutting, and the graphs showing the population change. Step 4: a) Vancouver Island Marmot Population 350 300 250 200 150 100 50 0 1980 1985 1990 1995 Year 672 • presentation is clear and matches the information found in the project Step 3: a) My data will include a table that shows the populations each year and a line graph that matches the data. Population 4. 20 000 1 5. a) b) That the chance of picking each type is equal. c) 5; 10% 5 d) Peoples’ preferences are not equally divided. • very clear • good • some • detailed description enough description description • analysis 3. a) 50 b) He assumed the sample was representative of the whole population. Level 4 • description • limited or of population not complete Analysing Practise Level 3 • fairly clear • mostly clear Communicate the Ideas 2. Experimental probability: Take a fair survey of soccer players to see their favourites. Theoretical probability: If 4 flavours are offered, the theoretical probability for each flavour is 25%. Level 2 • question and • not clear hypothesis Working Example 3: Show You Know a) Watching Movies: 50%; Bowling: 17.75% b) Answers may vary. Example: I would add up the totals for each activity to find the most commonly picked activity. 1. Answers may vary. Example: Taking too small a sample can result in a false prediction because it doesn’t give fair or true results. Level 1 2000 2005 b) I predict the population will continue to decline in the wild unless clearcutting is stopped. c) Answers will vary. 16. Answers may vary. Example: a) Her prediction is not reasonable because she only samples her class, which does not represent the whole school. b) 70% of the grade 9 students will vote for Nancy. Step 5: Answers will vary. Key Word Builder, page 660 Math Link: Wrap It Up!, page 654 Answers will vary. Examples: 1. sample 2. random 3. stratified 4. systematic 5. population 6. biased 7. voluntary 8. convenience Graphic Organizer, page 655 Answers will vary. Examples: Convenience sample Definition: choosing people who are easy to survey Example: the students in my class Voluntary response sample Definition: people who are invited to take the survey Example: an Internet site that asks readers to take a survey Stratified sample Definition: when the population is divided into groups and each group is fairly surveyed Example: 10 students are randomly surveyed from each grade in the school Systematic sample Definition: people on a list are fairly picked by their place on the list Example: every 20th person in the telephone book is surveyed Influencing factors Definition: factors that affect the responses in a survey Example: bias, language, ethics, cost, time and timing, privacy, cultural sensitivity Population Definition: all the individuals in the group being studied Example: the grade 12 population is all the students in grade 12 Chapter 11 Review, pages 656–659 1. systematic sample 2. influencing factors 3. biased sample 4. convenience sample 5. sample 6. random sample 7. population 8. stratified sample 9. voluntary response sample 10. a) time and timing b) bias c) bias 11. Answers may vary. Example: a) use of language; Do you support more money for hospitals? Yes or No. b) bias; Do you listen to rock music? Yes or No. If yes, who is your favourite rock group? c) use of language; If you had to pick between the two, would you prefer to have snack after school or to play a sport? 12. a) teens in Canada; randomly sampling high school students from across Canada b) students at our school; randomly select 20 students from each grade c) members of our community; systematically survey every 20th person in community phone book 13. a) convenience; people entering from the north side might be from a particular neighbourhood that doesn’t represent the mall population of shoppers b) stratified; smaller provinces are over represented c) convenience; the supervisor might only pick employees she likes 14. a) systematic sample; surveying every tenth customer would give a random sample b) stratified sample; surveying 10% of doctors, nurses, and administrators would be representative of the population 1 15. a) 8 people chose Candidate B. b) ; Each candidate has an equal chance 3 of being voted for. c) The experimental probability is greater than the theoretical probability by about 17%. d) YES; The survey predicted candidate A will receive the most votes by far. S T N G R E E F E Y X O L D F C Y Y Q X E A M C Q Q Q C R E W B I A S E D N N B V X T B S C Y D H M E R G E C N M Q G T L I R J K I S A I Y J Q V J R U S T R N Y X E N P W O R V A R A K A L N V W E D L N Y F T W M I X M J W Q V U O Z R D I R P M Z C E F D N G K M V V F Z L T Z I B T T O H C Y P G I Y E L Y S V A S C I W Y Z T E U Z R G H R T X Y X U N I K D X V D A Y T L X Y S M Q V U I N O I T A L U P O P N M A L Z J X U F K K V Z K J V F Q E Y Chapter 11 Practice Test, pages 661–662 1. A 2. C 3. B 4. D 5. sample 6. systematic sample 7. voluntary response sample 8. a) students in her high school b) Answers will vary. Example: Which type of music would you most like played at the school dance? Choose rap, alternative, rock, or country. c) Cheyenne could do a stratified sample by selecting 20 students from each grade. 9. a) 97 cellphones would be defective. b) The sample represents the population. Challenge, page 663 Answers will vary. Example: 1. a) Data from Vancouver International Airport: Year Mean Annual Temperature (°C) 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 11.3 10.2 10.1 10.2 10.3 10.9 11.5 10.8 10.6 10.2 b) Mean Annual Temperature (ºC) 11.6 11.4 11.2 Temperature Step 6: a) Marmots are being bred in zoos with the hope that they can be reintroduced into the wild. b) There are so few left they are difficult to find. c) The government could protect marmot habitat so they have a place to live. d) No. There are too few left to repopulate without human help. e) The Vancouver Island marmot is almost extinct and needs a lot of help to survive. f) Scientists should find a way to reintroduce marmots into the wild. g) The main type of sampling is systematic. Scientists could sample the whole population. 11 10.8 10.6 10.4 10.2 10 1996 1998 2000 2002 2004 2006 2008 Year 2. a) No, there is not a warming trend because the temperatures ended up lower than where they started. b) These findings do not support global warming because the temperatures did not show any sort of trend. Answers ● MHR 673 Chapters 8–11 Review, pages 664–670 1 15 1 1. a) x = or 7 b) x = 20 2 2 10. x ≥ 4.5 or 9 1 or 4 2 2 2. The height is 3.4 m. 11. a) Variable: h = the number of hours; Inequality: 145h ≤ 800 b) h ≤ 5.5; Lori can rent the wall for 5.5 or fewer hours. 3. He paid $3.49 for each box. 12. a) 47° b) 94° 4. They charge the same amount for a 2.5 h service call. 13. 5.4 5. The side length of the square is 21 units. 3 6. a) x ≤ 17 b) x ≥ – 6 and x < –5 5 14. 48 7. a) 16. a) students b) Answers will vary. Example: convenience sample, systematic sample b) -8 1 -7 -6 -5 2 3 8. a) ≥ b) Variable: Let s = budget surplus. Inequality: s > 1.3 million 9. a) x < 8.8 b) x > –5 c) x ≥ –50 d) x ≥ 12 674 MHR ● Chapter 11: Data Analysis 15. a) bias; Do you play cards? b) bias; Would you prefer a band or a DJ at the dance? 1 b) Every activity has an equal chance of being 5 chosen. Customers have an equal interest in each activity. c) 12, 24% d) Customers do not have an equal interest in each activity. 17. a) P(swimming) =