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(1)Data Analysis Analysis. Notes Introduction In this unit, students will learn how to analyze data using statistical analysis. This includes understanding sampling techniques, histograms, and box-and-whisker plots. Students will then learn how to use probability to predict outcomes.. Assessment Options. Collecting and analyzing data allows you to make decisions and predictions about the future. In this unit, you will learn about statistics and probability.. Unit 5 Test Pages 881–882 of the Chapter 14 Resource Masters may be used as a test or review for Unit 5. This assessment contains both multiple-choice and short answer items.. TestCheck and Worksheet Builder. Chapter 13. This CD-ROM can be used to create additional unit tests and review worksheets.. Statistics. Chapter 14 Probability. 704 Unit 5 Data Analysis. 704. Unit 5 Data Analysis.

(2) Teaching Suggestions Have students study the USA TODAY Snapshot. • Ask students what they can determine from the data in the graph. The population of the United States grew by 149 million in the 60 years from 1940 to 2000. • What might be needed to predict the population of the United States in the year 2050? Sample answer: More information about the population growth rate and how much it has increased annually. Additional USA TODAY Snapshots appearing in Unit 5: Chapter 13 Cheaper wireless talk (p. 730) Chapter 14 Women follow football on TV (p. 780). America Counts! The U.S. government has been counting each person in the country since its first Census following independence was taken in 1790. Befitting the first Census of the 21st century, the Census Bureau allowed Census 2000 questionnaires to be completed electronically for the first time. In this project, you will see how data analysis can be used to compare statistics about a state of your choice to other states in the United States.. USA TODAY Snapshots® U.S. population growth The U.S. population has more than doubled since 1940. 281 million. U05-001C-USA. 132 million. Log on to www.algebra1.com/webquest. Begin your WebQuest by reading the Task. Then continue working on your WebQuest as you study Unit 5.. Lesson Page. 13-5 742. 14-2 766. 1940. 2000. Source: U.S. Census Bureau. By Marcy E. Mullins, USA TODAY. Unit 5. Data Analysis. 705. Internet Project A WebQuest is an online project in which students do research on the Internet, gather data, and make presentations using word processing, graphing, page-making, or presentation software. In each chapter, students advance to the next step in their WebQuest. At the end of Chapter 14, the project culminates with a presentation of their findings. Teaching notes and sample answers are available in the WebQuest and Project Resources. Unit 5. Data Analysis 705.

(3) Statistics Chapter Overview and Pacing. PACING (days) Regular Block. LESSON OBJECTIVES. Basic/ Average. Advanced. Basic/ Average. Advanced. Sampling and Bias (pp. 708–713) • Identify various sampling techniques. • Recognize a biased sample.. optional. 2. optional. 1.5. Introduction to Matrices (pp. 715–721) • Organize data in matrices. • Solve problems by adding or subtracting matrices or by multiplying by a scalar.. optional. 2. optional. 1. Histograms (pp. 722–730) • Interpret data displayed in histograms. • Display data in histograms. Follow-Up: Use a graphing calculator to find an appropriate regression equation.. optional. 2. optional. 1. Measures of Variation (pp. 731–736) • Find the range of a set of data. • Find the quartiles and interquartile range of a set of data.. optional. 2. optional. 1. Box-and-Whisker Plots (pp. 737–744) • Organize and use data in box-and-whisker plots. • Organize and use data in parallel box-and-whisker plots. Follow-Up: Use tables to determine percentiles.. optional. 3. optional. 1.5. Study Guide and Practice Test (pp. 745–749) Standardized Test Practice (pp. 750–751). optional. 1. optional. 0.5. Chapter Assessment. optional. 1. optional. 0.5. TOTAL. Pacing suggestions for the entire year can be found on pages T20–T21.. 706A Chapter 13 Statistics. 13. 7.

(4) Timesaving Tools ™. All-In-One Planner and Resource Center. Chapter Resource Manager. 781–782. 783–784. 785. 786. 787–788. 789–790. 791. 792. 825. 793–794. 795–796. 797. 798. 825, 827. 97–98. 799–800. 801–802. 803. 804. 826. 1–2, 19–20. 805–806. 807–808. 809. 810. 826. Ap plic atio ns* Par Stu ent dy a Gu nd St ide u Wo dent rkb 5-M ook Tra inute nsp Che are nci ck es Int e Cha racti lkb ve oar d Alg ePA Plu SS: T s (l ess utoria ons l ). Ass ess me nt Pre req u Wo isite rkb Ski ook lls. Enr ich me nt. S and tudy Int Guid erv e ent ion (Sk Pra c ills and tice. Ave rag e). Rea di Ma ng to the ma Learn tics. CHAPTER 13 RESOURCE MASTERS. See pages T12–T13.. Materials. 101. 13-1. 13-1. GCS 47. 102. 13-2. 13-2. graphing calculator. GCS 48, SC 25. 103. 13-3. 13-3. graphing calculator, (Follow-Up: graphing calculator). 104. 13-4. 13-4. 105. 13-5. 13-5. SC 26, SM 103–108. 811–824, 828–830. 34. (Preview: ruler). 106. *Key to Abbreviations: GCS Graphing Calculator and Speadsheet Masters, SC School-to-Career Masters, SM Science and Mathematics Lab Manual. ELL Study Guide and Intervention, Skills Practice, Practice, and Parent and Student Study Guide Workbooks are also available in Spanish. Chapter 13 Statistics 706B.

(5) Mathematical Connections and Background Continuity of Instruction Prior Knowledge Students were introduced to analyzing data in tables and graphs, and to determining whether these data are misleading in Chapter 1. In Chapter 2, students learned to add, subtract, and multiply real numbers and how to represent data in line plots and stemand-leaf plots. They also learned to use the mean, median, and mode of data sets. In Chapter 5, students interpreted scatter plots and found lines of fit.. This Chapter Students go beyond what they have already learned about statistics by identifying various sampling techniquesand interpreting data. They learn how to organize data in matrices, and manipulate the data by adding and subtracting matrices, or by scalar multiplication. Students then interpret data in histograms, and find the range, quartiles, and interquartile ranges of data sets. Finally students organize and use data in boxand-whisker plots.. Future Connections Whether on television, in newspapers, or on the Internet, statistics are used to sway public opinion, to inform, or to persuade the public to buy a product. Being able to interpret these statistics is important to being able to make sound decisions. The decisions made based on statistics vary from the trivial, such as what shampoo to buy, to the most important, such as who to vote for in an upcoming election.. 706C. Chapter 13 Statistics. Sampling and Bias To understand sampling techniques, students must first understand that a sample is a small portion of a larger group called a population. Samples are taken to represent a group because they are smaller and easier to survey. If an entire population is included in a sample, it is a census. Samples are used to find preferences or characteristics of a population. A sample that is chosen without preference is a random sample. Random samples are chosen in different ways. A simple random sample is exactly as it sounds, with members picked at random from a population without bias. If a population is first segregated into non-overlapping groups, from which random samples are taken, then it is a stratified random sample. An example would be if an algebra teacher randomly chose three people from each of his of her classes. A systematic random sample is picked by following a certain pattern, such as picking every fifth person who walks by. Samples are biased if they favor one or more parts of a population. Biased samples include convenience samples, in which members of the sample are picked because they are convenient for the person taking the sample. Another example of a biased sample is a voluntary response sample. It is biased because the members of the sample only replied if they wanted to be included.. Introduction to Matrices A matrix is a rectangular array of numerical data arranged in regular rows and columns. The dimensions of a matrix are the number of rows and columns in the matrix. Each entry in a matrix is called an element. If two matrices have the same dimensions, then they can be added or subtracted by adding or subtracting the corresponding elements of the two matrices. If their dimensions are not the same, then they cannot be added or subtracted. Matrices can also be multiplied by a single real number called a scalar. In scalar multiplication, each member of a matrix is multiplied by the same scalar..

(6) Histograms Imagine surveying 20 people leaving a shopping mall and finding out that 4 have spent $100 or more, but less than $150. Six have spent $50 or more, but less than $100, and 10 have spent less than $50. These data can be represented in a two-column frequency table. The left column has three intervals, $0–$50, $50–$100, and $100–$150. Then the next column shows the number of people who fit into each category. Each person is counted with a tally mark. The amount represented by the tallies for a category is called the frequency for each category. Now display the data from the frequency table as a bar graph. The horizontal axis would correspond to the left column of the table, showing three measurement classes; $0–$50, $50–$100, and $100–$150. These must be organized in equal intervals. The vertical axis would correspond to the right column, and would display the frequency for each measurement class. This graph is known as a histogram. Histograms are used to compare data visually. You can quickly determine form looking at the bars which measurement class has the most, the least, etc.. Box-and-Whisker Plots Use a box-and-whisker plot to graphically represent the measures of variation on a number line. The box portion of a box-and-whisker plot extends from the lower quartile to the upper quartile, with the median denoted within the box. The box represents the interquartile range. The whiskers extend from the lower quartile to the least value, and from the upper quartile to the greatest value. If either the greatest or least values are outliers, then the whiskers extend to the least or greatest values that are not outliers. The ends of the whiskers are the extreme values. Two sets of data can be compared by drawing two box-and-whisker plots above the same number line. This display is called parallel box-and-whisker plots.. Measures of Variation Knowing how a set of data varies is often very helpful in interpreting the data. Mean, median, and mode, which were studied in Chapter 2, are measures of central tendency. Measures that describe the spread of the values in a set of data are called measures of variation. One such measure is the range, which is the difference between the greatest and least data values. Quartiles are another measure of variation. They are values that separate the data into four equal subsets. The lower quartile separates the lower half of the data into two equal parts. The upper quartile separates the upper half of the data into two equal parts. The interquartile range is the difference between the upper and lower quartiles. An outlier is a value in a set of data that is much less or much greater than the rest of the data.. Chapter 13 Statistics 706D.

(7) and Assessment. ASSESSMENT. INTERVENTION. Type. Student Edition. Teacher Resources. Ongoing. Prerequisite Skills, pp. 707, 721, 728, 736 Practice Quiz 1, p. 721 Practice Quiz 2, p. 736. 5-Minute Check Transparencies Prerequisite Skills Workbook, pp. 1–2, 19–20, 97–98 Quizzes, CRM pp. 825–826 Mid-Chapter Test, CRM p. 827 Study Guide and Intervention, CRM pp. 781–782, 787–788, 793–794, 799–800, 805–806. Mixed Review. pp. 713, 721, 728, 736, 742. Cumulative Review, CRM p. 828. Error Analysis. Find the Error, pp. 717, 733. Find the Error, TWE pp. 717, 733 Unlocking Misconceptions, TWE pp. 725, 732, 738 Tips for New Teachers, TWE p. 724. Standardized Test Practice. pp. 713, 720, 723, 724, 726, 728, 736, 742, 749, 750–751. TWE pp. 750–751 Standardized Test Practice, CRM pp. 829–830. Open-Ended Assessment. Writing in Math, pp. 713, 720, 728, 736, 742 Open Ended, pp. 710, 717, 725, 733, 739 Standardized Test, p. 751. Modeling: TWE p. 728 Speaking: TWE pp. 713, 736 Writing: TWE pp. 721, 742 Open-Ended Assessment, CRM p. 823. Chapter Assessment. Study Guide, pp. 745–748 Practice Test, p. 749. Multiple-Choice Tests (Forms 1, 2A, 2B), CRM pp. 811–816 Free-Response Tests (Forms 2C, 2D, 3), CRM pp. 817–822 Vocabulary Test/Review, CRM p. 824. Technology/Internet AlgePASS: Tutorial Plus www.algebra1.com/self_check_quiz www.algebra1.com/extra_examples. Standardized Test Practice CD-ROM www.algebra1.com/ standardized_test. TestCheck and Worksheet Builder (see below) MindJogger Videoquizzes www.algebra1.com/ vocabulary_review www.algebra1.com/chapter_test. Key to Abbreviations: TWE = Teacher Wraparound Edition; CRM = Chapter Resource Masters. Additional Intervention Resources The Princeton Review’s Cracking the SAT & PSAT The Princeton Review’s Cracking the ACT ALEKS. TestCheck and Worksheet Builder This networkable software has three modules for intervention and assessment flexibility: • Worksheet Builder to make worksheet and tests • Student Module to take tests on screen (optional) • Management System to keep student records (optional) Special banks are included for SAT, ACT, TIMSS, NAEP, and End-of-Course tests.. 706E. Chapter 13 Statistics.

(8) Reading and Writing in Mathematics Intervention Technology AlgePASS: Tutorial Plus CD-ROM offers a complete, self-paced algebra curriculum. Algebra 1 Lesson 13-5. AlgePASS Lesson 34 Integration: Introduction to Statistics. ALEKS is an online mathematics learning system that adapts assessment and tutoring to the student’s needs. Subscribe at www.k12aleks.com.. Intervention at Home Parent and Student Study Guide Parents and students may work together to reinforce the concepts and skills of this chapter. (Workbook, pp. 101–106 or log on to www.algebra1.com/parent_student ) Log on for student study help. • For each lesson in the Student Edition, there are Extra Examples and Self-Check Quizzes. www.algebra1.com/extra_examples www.algebra1.com/self_check_quiz. • For chapter review, there is vocabulary review, test practice, and standardized test practice. www.algebra1.com/vocabulary_review www.algebra1.com/chapter_test www.algebra1.com/standardized_test. For more information on Intervention and Assessment, see pp. T8–T11.. Glencoe Algebra 1 provides numerous opportunities to incorporate reading and writing into the mathematics classroom. Student Edition • Foldables Study Organizer, p. 707 • Concept Check questions require students to verbalize and write about what they have learned in the lesson. (pp. 710, 717, 725, 733, 739) • Reading Mathematics, p. 714 • Writing in Math questions in every lesson, pp. 713, 720, 728, 736, 742 • Reading Study Tip, pp. 732, 737 • WebQuest, p. 742 Teacher Wraparound Edition • Foldables Study Organizer, pp. 707, 745 • Study Notebook suggestions, pp. 711, 714, 718, 725, 734, 740, 744 • Modeling activities, p. 728 • Speaking activities, pp. 713, 736 • Writing activities, pp. 721, 742 • Differentiated Instruction, (Verbal/Linguistic), p. 720 • ELL Resources, pp. 706, 712, 714, 719, 720, 726, 735, 741, 745 Additional Resources • Vocabulary Builder worksheets require students to define and give examples for key vocabulary terms as they progress through the chapter. (Chapter 13 Resource Masters, pp. vii-viii) • Reading to Learn Mathematics master for each lesson (Chapter 13 Resource Masters, pp. 785, 791, 797, 803, 809) • Vocabulary PuzzleMaker software creates crossword, jumble, and word search puzzles using vocabulary lists that you can customize. • Teaching Mathematics with Foldables provides suggestions for promoting cognition and language. • Reading and Writing in the Mathematics Classroom • WebQuest and Project Resources • Hot Words/Hot Topics Sections 2.6, 4.1–4.4, 5.2. For more information on Reading and Writing in Mathematics, see pp. T6–T7. Chapter 13 Statistics 706F.

(9) Notes Have students read over the list of objectives and make a list of any words with which they are not familiar.. Point out to students that this is only one of many reasons why each objective is important. Others are provided in the introduction to each lesson.. Statistics • Lesson 13-1 Identify various sampling techniques. • Lesson 13-2 Solve problems by adding or subtracting matrices or by multiplying by a scalar. • Lesson 13-3 Interpret data displayed in histograms. • Lesson 13-4 Find the range, quartiles, and interquartile range of a set of data. • Lesson 13-5 Organize and use data in box-and-whisker plots.. Key Vocabulary • • • • •. sample (p. 708) matrix (p. 715) histogram (p. 722) quartile (p. 732) box-and-whisker plot (p. 737). Each day statistics are reported in the newspapers, in magazines, on television, and on the radio. These data involve business, government, ecology, sports, and many other topics. A basic knowledge of statistics allows you to interpret what you hear and read in the media. One important tool to help you understand the significance of a set of data is the box-and-whisker plot. You will draw and use a box-and-whisker plot for data involving NASCAR racing in Lesson 13-5.. Lesson 13-1 13-2 13-3 13-3 Follow-Up 13-4 13-5 13-5 Follow-Up. NCTM Standards. Local Objectives. 1, 5, 6, 8, 9 1, 5, 6, 8, 9, 10 1, 5, 6, 8, 9, 10 5, 6, 8, 9 1, 5, 6, 8, 9, 10 1, 5, 6, 8, 9, 10 1, 5, 6, 9, 10. Key to NCTM Standards: 1=Number & Operations, 2=Algebra, 3=Geometry, 4=Measurement, 5=Data Analysis & Probability, 6=Problem Solving, 7=Reasoning & Proof, 8=Communication, 9=Connections, 10=Representation 706. Chapter 13 Statistics. 706 Chapter 13 Statistics. Vocabulary Builder. ELL. The Key Vocabulary list introduces students to some of the main vocabulary terms included in this chapter. For a more thorough vocabulary list with pronunciations of new words, give students the Vocabulary Builder worksheets found on pages vii and viii of the Chapter 13 Resource Masters. Encourage them to complete the definition of each term as they progress through the chapter. You may suggest that they add these sheets to their study notebooks for future reference when studying for the Chapter 13 test..

(10) Prerequisite Skills To be successful in this chapter, you’ll need to master these skills and be able to apply them in problem-solving situations. Review these skills before beginning Chapter 13. For Lesson 13-1. Use Logical Reasoning. Find a counterexample for each statement. (For review, see Lesson 1-7.) 1. If a b c, then a c. Sample answer: If a 5 and b 2, then c 3. However, 5 3. 2. If a flower is a rose, then it is red. Sample answer: It could be a yellow rose. 3. If Tara obeys the speed limit, then she will drive 45 miles per hour or less. 4. If a number is even, then it is divisible by 4.. Sample answer: 6 is even, but not divisible by 4.. 3. Sample answer: The speed limit could be 55 mph, and Tara could be driving 50 mph.. For Lesson 13-4. Find the Median. Find the median for each set of data.. (For review, see pages 818 and 819.). 5. 1, 7, 9, 15, 25, 59, 63 15. This section provides a review of the basic concepts needed before beginning Chapter 13. Page references are included for additional student help. Additional review is provided in the Prerequisite Skills Workbook, pp. 1–2, 19–20, and 97–98. Prerequisite Skills in the Getting Ready for the Next Lesson section at the end of each exercise set review a skill needed in the next lesson.. 6. 0, 10, 2, 2, 9, 5, 4, 2, 8, 3, 8, 7, 3 4 7. 726, 411, 407, 407, 395, 355, 317, 235, 218, 211 375. For Lesson 13-5. For Lesson. Prerequisite Skill. 13-2. Finding Sums and Differences, p. 713 Interpreting Graphs, p. 721 Finding the Median, p. 728 Graphing Numbers on a Number Line, p. 736. Graph Numbers on a Number Line. Graph each set of numbers on a number line. (For review, see Lesson 2-1.) 8–11. See margin. 8. {7, 9, 10, 13, 14}. 13-3 13-4 13-5. 9. {15, 17.5, 19, 20.5, 23}. 10. {3.2, 4.8, 5.0, 5.7, 6.1}. 11. {2.3, 2.8, 3.1, 3.7, 4.5}. Make this Foldable to help you organize information about 1 statistics. Begin with three sheets of plain 8" by 11" paper. 2. Answers 8. 7 8 9 10 11 12 13 14 15. Stack Pages. Fold Up Bottom Edges. 9. 15 16 17 18 19 20 21 22 23. All tabs should be the same size.. Stack sheets of paper with edges 3 inch apart.. 10.. 4. 3. 4. 5. 6. 7. 1. 2. 3. 4. 5. 11. Crease and Staple Staple along fold.. Turn and Label Label the tabs with topics from the chapter.. Reading and Writing. Statistics 13-1 Sampling and Bias 13-2 Matrices 13-3 Histograms 13-4 Measures of Variation 13-5 Box-and-Whisker Plots. As you read and study the chapter, use each page to write. notes and examples.. Chapter 13 Statistics 707. TM. For more information about Foldables, see Teaching Mathematics with Foldables.. Organization of Data and Statistics in Writing Students use their Foldables to take notes, define terms, record concepts, and write examples. On the back of the Foldable, have students record examples of statistics they see in everyday print—newspapers, magazines, and advertisements. Note how writers use statistics to prove or disprove points of view, and discuss the ethical responsibilities writers have when using statistics.. Chapter 13 Statistics 707.

(11) Lesson Notes. 1 Focus 5-Minute Check Transparency 13-1 Use as a quiz or review of Chapter 12. Mathematical Background notes are available for this lesson on p. 706C. is sampling important in manufacturing? Ask students: • Suppose the manufacturer produces 100 CDs an hour, and takes a sample every hour. How many CDs would be sampled in an 8-hour day? 8 • What is an example of something you would sample at home? Sample answer: While cooking, you might sample gravy to check that it tastes good.. Sampling and Bias • Identify various sampling techniques. • Recognize a biased sample.. is sampling important in manufacturing?. Vocabulary • • • • • • •. sample population census random sample simple random sample stratified random sample systematic random sample • biased sample • convenience sample • voluntary response sample. Manufacturing music CDs involves burning, or recording, copies from a master. However, not every burn is successful. It is costly and time-consuming to check every CD that is burned. Therefore, in order to monitor production, some CDs are picked at random and checked for defects.. SAMPLING TECHNIQUES When you wish to make an investigation, there are four ways that you can collect data. • published data Use data that are already in a source like a newspaper or book. • observational study Watch naturally occurring events and record the results. • experiment Conduct an experiment and record the results. • survey Ask questions of a group of people and record the results. When performing an experiment or taking a survey, researchers often choose a sample. A sample is some portion of a larger group, called the population, selected to represent that group. If all of the units within a population are included, it is called a census. Sample data are often used to estimate a characteristic within an entire population, such as voting preferences prior to elections. Population. Sample. all of the light bulbs manufactured on a production line. 24 light bulbs selected from the production line. all of the water in a swimming pool. a test tube of water from the pool. all of the people in the United States. 1509 people from throughout the United States. A random sample of a population is selected so that it is representative of the entire population. The sample is chosen without any preference. There are several ways to pick a random sample.. Random Samples Random Samples Type. Definition. Example. Simple Random Sample. A simple random sample is a sample that is as likely to be chosen as any other from the population.. The 26 students in a class are each assigned a different number from 1 to 26. Then three of the 26 numbers are picked at random.. Stratified Random Sample. In a stratified random sample, the population is first divided into similar, nonoverlapping groups. A simple random sample is then selected from each group.. The students in a school are divided into freshman, sophomores, juniors, and seniors. Then two students are randomly selected from each group of students.. Systematic Random Sample. In a systematic random sample, the items are selected according to a specified time or item interval.. Every 2 minutes, an item is pulled off the assembly line. or Every twentieth item is pulled off the assembly line.. 708. Chapter 13 Statistics. Resource Manager Workbook and Reproducible Masters Chapter 13 Resource Masters • Study Guide and Intervention, pp. 781–782 • Skills Practice, p. 783 • Practice, p. 784 • Reading to Learn Mathematics, p. 785 • Enrichment, p. 786. Parent and Student Study Guide Workbook, p. 101. Transparencies 5-Minute Check Transparency 13-1 Answer Key Transparencies. Technology Interactive Chalkboard.

(12) Example 1 Classify a Random Sample ECOLOGY Ten lakes are selected randomly from a list of all public-access lakes in Minnesota. Then 2 liters of water are drawn from 20 feet deep in each of the ten lakes. a. Identify the sample and suggest a population from which it was selected. The sample is ten 2-liter containers of lake water, one from each of 10 lakes. The population is lake water from all of the public-access lakes in Minnesota. This is a simple random sample. Each of the ten lakes was equally likely to have been chosen from the list.. BIASED SAMPLE Random samples are unbiased. In a biased sample , one or more parts of a population are favored over others.. Ecology. Identify each sample as biased or unbiased. Explain your reasoning.. More than one twentieth of the area of Minnesota is covered by inland lakes. The largest lake is Red Lake, which covers 430 square miles.. a. MANUFACTURING Every 1000th bolt is pulled from the production line and measured for length. The sample is chosen using a specified time interval. This is an unbiased sample because it is a systematic random sample. b. MUSIC Every tenth customer in line for a certain rock band’s concert tickets is asked about his or her favorite rock band. The sample is a biased sample because customers in line for concert tickets are more likely to name the band giving the concert as a favorite band. Two popular forms of samples that are often biased include convenience samples and voluntary response samples.. Biased Samples Type. Definition. Convenience Sample. A convenience sample includes members of a population that are easily accessed.. To check spoilage, a produce worker selects 10 apples from the top of the bin. The 10 apples are unlikely to represent all of the apples in the bin.. A voluntary response sample involves only those who want to participate in the sampling.. A radio call-in show records that 75% of its 40 callers voiced negative opinions about a local football team. Those 40 callers are unlikely to represent the entire local population. Volunteer callers are more likely to have strong opinions and are typically more negative than the entire population.. Example. Example 3 Identify and Classify a Biased Sample BUSINESS The travel account records from 4 of the 20 departments in a corporation are to be reviewed. The accountant states that the first 4 departments to voluntarily submit their records will be reviewed. a. Identify the sample and suggest a population from which it was selected. The sample is the travel account records from 4 departments in the corporation. The population is the travel account records from all 20 departments in the corporation.. www.algebra1.com/extra_examples. Lesson 13-1 Sampling and Bias. 709. Teacher to Teacher Patricia Taepke. In-Class Example. Power Point®. Remind students that the sample is what is taken, and the population is the group from which the sample is taken. A population does not have to be a group of people.. 1 RETAIL Each day, a depart-. Example 2 Identify Sample as Biased or Unbiased. Voluntary Response Sample. SAMPLING TECHNIQUES. Teaching Tip. b. Classify the sample as simple, stratified, or systematic.. Source: World Book Encyclopedia. 2 Teach. South Hills H.S., West Covina, CA. "I copy pages 708 and 709 for my students to place in their Algebra 1 Study Notebooks. These pages contain a great deal of vocabulary that they may use for future reference. It is arranged in a very concise manner.". ment store chain selects one male and one female shopper randomly from each of their 57 stores, and asks them survey questions about their shopping habits. a. Identify the sample and suggest a population from which it was selected. The sample is 57 male and 57 female shoppers each day. The population is shoppers in the chain’s stores. b. Classify the sample as simple, stratified, or systematic. This is a stratified random sample.. BIASED SAMPLE. In-Class Example. Power Point®. 2 Identify each sample as biased or unbiased. Explain your reasoning. a. STUDENT COUNCIL The student council surveys the students in one classroom to decide the theme for the spring dance. The sample is biased because it includes only the students in one classroom. b. SCHOOL The Parent Association surveys the parents of every fifth student on the school roster to decide whether to hold a fundraiser. The sample is unbiased because the parents are picked using a systematic method.. Lesson 13-1 Sampling and Bias 709.

(13) In-Class Examples. b. Classify the sample as convenience or voluntary response.. Power Point®. Since the departments voluntarily submit their records, this is a voluntary response sample.. 3 COMMUNITY The maintenance chairperson of a neighborhood association has been asked by the association to survey the residents of the neighborhood to find out when to hold a neighborhood clean up day. The chairperson decides to ask her immediate neighbors, and the neighbors in the houses directly across the street from her house.. Example 4 Identify the Sample NEWS REPORTING For an article in the school paper, Rafael needs to determine whether students in his school believe that an arts center should be added to the school. He polls 15 of his friends who sing in the choir. Twelve of them think the school needs an arts center, so Rafael reports that 80% of the students surveyed support the project. a. Identify the sample. The sample is a group of students from the choir. b. Suggest a population from which the sample was selected. The population for the survey is all of the students in the school. c. State whether the sample is unbiased (random) or biased. If unbiased, classify it as simple, stratified, or systematic. If biased, classify it as convenience or voluntary response.. a. Identify the sample, and suggest a population from which it was selected. The sample is the chairperson’s immediate neighbors and the neighbors across the street. The population is the residents of the neighborhood.. The sample was not randomly selected from the entire student body. So the reported support is not likey to be representative of the student body. The sample is biased. Since Rafael polled only his friends, it is a convenience sample.. Concept Check. b. Classify the sample as a convenience sample, or a voluntary response sample. This is a convenience sample because the chairperson asked only her closest neighbors.. • simple random sample • stratified random sample • systematic random sample 2. Explain the difference between a convenience sample and a voluntary response sample. See margin.. 4 SCHOOL The high school Parent Association sent a letter to the parents of all graduating seniors asking them to return the enclosed ballot if they had a preference on where the graduation party was to be held. a. Identify the sample. The sample is a group of parents of the graduating seniors. b. Suggest a population from which the sample was selected. The population is all the parents of the graduating seniors. c. State whether the sample is unbiased (random) or biased. If unbiased, classify it as simple, stratified, or systematic. If biased, classify it as convenience or voluntary response. The sample is biased. It is a voluntary response sample.. 710. Chapter 13 Statistics. 1. Describe how the following three types of sampling techniques are similar and how they are different. See margin.. 3. OPEN ENDED Give an example of a biased sample. Sample answer: Ask the. members of the school’s football team to name their favorite sport.. Guided Practice. GUIDED PRACTICE KEY Exercises. Examples. 4–7. 1–4. 4. a group of readers of a newspaper; all readers of the newspaper; biased; voluntary response 5. work from 4 students; work from all students in the 1st period math class; biased; voluntary response 710. Chapter 13 Statistics. Identify each sample, suggest a population from which it was selected, and state whether it is unbiased (random) or biased. If unbiased, classify the sample as simple, stratified, or systematic. If biased, classify as convenience or voluntary response. 4. NEWSPAPERS The local newspaper asks readers to write letters stating their preferred candidate for mayor. 5. SCHOOL A teacher needs a sample of work from 4 students in her first-period math class to display at the school open house. She selects the work of the first 4 students who raise their hands. 6. BUSINESS A hardware store wants to assess the strength of nails it sells. Store personnel select 25 boxes at random from among all of the boxes on the shelves. From each of the 25 boxes, they select one nail at random and subject it to a strength test. 25 nails; all nails on the store shelves; unbiased; stratified 7. SCHOOL A class advisor hears complaints about an incorrect spelling of the school name on pencils sold at the school store. The advisor goes to the store and asks Namid to gather a sample of pencils and look for spelling errors. Namid grabs the closest box of pencils and counts out 12 pencils from the top of the box. She checks the pencils, returns them to the box, and reports the results to the advisor.. 12 pencils; all pencils in the school store; biased; convenience. Differentiated Instruction Visual/Spatial Place students in small groups. Give each group a number of different colored beads to serve as a population. Then, have the groups model the different types of random samples with the beads. For example, for stratified random samples, students must first divide the beads into groups by color and then take random beads from each group. Have students describe how they would take a systematic random sample..

(14) ★ indicates increased difficulty. Practice and Apply Homework Help For Exercises. See Examples. 8–28. 1–4. Extra Practice See page 849.. Identify each sample, suggest a population from which it was selected, and state whether it is unbiased (random) or biased. If unbiased, classify the sample as simple, stratified, or systematic. If biased, classify as convenience or voluntary response. 8. SCHOOL Pieces of paper with the names of 3 sophomores are drawn from a hat containing identical pieces of paper with all sophomores’ names.. 3 sophomores; all sophomores in the school; unbiased; simple 9. FOOD Twenty shoppers outside a fast-food restaurant are asked to name their preferred cola among two choices. 20 shoppers; all shoppers; biased; convenience 10. RECYCLING An interviewer goes from house to house on weekdays between 9 A.M. and 4 P.M. to determine how many people recycle. people who are home. between 9 A.M. and 4 P.M.; all people in the neighborhood; biased; convenience 11. POPULATION A state is first divided into its 86 counties and then 10 people from each county are chosen at random.. 860 people from a state; all people in the state; unbiased; stratified 12. SCOOTERS A scooter manufacturer is concerned about quality control. The manufacturer checks the first 5 scooters off the line in the morning and the last 5 off the line in the afternoon for defects. 10 scooters; all scooters manufactured. on a particular production line during one day; biased; convenience 13. SCHOOL To determine who will speak for her class at the school board meeting, Ms. Finchie used the numbers appearing next to her students’ names in her grade book. She writes each of the numbers on an identical piece of paper and shuffles the pieces of papers in a box. Without seeing the contents of the box, one student draws 3 pieces of paper from the box. The students whose numbers match the numbers chosen will speak for the class.. 3 Practice/Apply Study Notebook Have students— • add the definitions/examples of the vocabulary terms to their Vocabulary Builder worksheets for Chapter 13. • include explanations on how to identify whether a sample is random, the type of random sample, and whether the sample is biased. • include any other item(s) that they find helpful in mastering the skills in this lesson.. 3 students; all of the students in Ms. Finchie’s class; unbiased; simple 14. FARMING An 8-ounce jar was filled with corn from a storage silo by dipping the jar into the pile of corn. The corn in the jar was then analyzed for moisture content. an 8-oz jar of corn; all corn in the storage silo; biased; convenience 15. COURT The gender makeup of district court judges in the United States is to be estimated from a sample. All judges are grouped geographically by federal reserve districts. Within each of the 11 federal reserve districts, all judges’ names are assigned a distinct random number. In each district, the numbers are then listed in order. A number between 1 and 20 inclusive is selected at random, and the judge with that number is selected. Then every 20th name after the first selected number is also included in the sample. a group of U.S. district court. judges; all U.S. district court judges; unbiased; stratified. Food Michigan leads the nation in cherry production by growing about 219 million pounds of cherries per year. Source: World Book Encyclopedia. 19. a group of high-definition television sets; all high-definition television sets manufactured on one line during one shift; unbiased; systematic. 16. TELEVISION A television station asks its viewers to share their opinions about a proposed golf course to be built just outside the city limits. Viewers can call one of two 900-numbers. One number represents a “yes” vote, and the other number represents a “no” vote. a group of people who watch a television. station; all people who watch the television station; biased; voluntary response 17. GOVERNMENT To discuss leadership issues shared by all United States Senators, the President asks 4 of his closest colleagues in the Senate to meet with him. 4 U.S. Senators; all U.S. Senators; biased; convenience 18. FOOD To sample the quality of the Bing cherries throughout the produce department, the produce manager picks up a handful of cherries from the edge of one case and checks to see if these cherries are spoiled. a handful of Bing. About the Exercises… Odd/Even Assignments Exercises 8–21, 24, 25, 27, and 28 are structured so that students practice the same concepts whether they are assigned odd or even problems.. Assignment Guide Basic: 9–21 odd, 29–51 Average: 9–21 odd, 22, 23, 29–51 Advanced: 8–20 even, 22–45 (optional: 46–51). cherries; all Bing cherries in the produce department; biased; convenience 19. MANUFACTURING During the manufacture of high-definition televisions, units are checked for defects. Within the first 10 minutes of a work shift, a television is randomly chosen from the line of completed sets. For the rest of the shift, every 15th television on the line is checked for defects.. www.algebra1.com/self_check_quiz. Lesson 13-1 Sampling and Bias. 711. Answers 1. All three are unbiased samples. However, the methods for selecting each type of sample are different. In a simple random sample, a sample is as likely to be chosen as any other from the population. In a stratified random sample, the population is first divided into similar, nonoverlapping groups. Then a simple random sample is selected from each group. In a systematic random sample, the items are selected according to a specified time or item interval.. 2. A convenience sample is a biased sample that is determined based on the ease with which it is possible to gather the sample. A voluntary sample is a biased sample composed of voluntary responses. Lesson 13-1 Sampling and Bias 711.

(15) NAME ______________________________________________ DATE. Identify each sample, suggest a population from which it was selected, and state whether it is unbiased (random) or biased. If unbiased, classify the sample as simple, stratified, or systematic. If biased, classify as convenience or voluntary response.. ____________ PERIOD _____. Study Guide andIntervention Intervention, 13-1 Study Guide and p. 781 (shown) Sampling and Bias and p. 782. Sampling Techniques. Suppose you want to survey students about their choice of radio stations. All students make up the population you want to survey. A sample is some portion of the larger group that you select to represent the entire group. A census would include all students within the population. A random sample of a population is selected so that it is representative of the entire population. a sample that is as likely to be chosen as another from a population. Stratified Random Sample. A population is first divided into similar, nonoverlapping groups. A simple random sample is then chosen from each group.. Systematic Random Sample. Items are selected according to a specified time or interval.. Example 1. Example 2. SCHOOL Ten students. are chosen randomly from each high school class to be on an advisory committee with the principal. a. Identify the sample and suggest a population from which it was chosen. The sample is 4 groups of 10 students each from the freshmen, sophomore, junior, and senior classes. The population is the entire student body of the school. b. Classify the sample as simple, stratified, or systematic. This is a stratified random sample because the population was first divided into nonoverlapping groups and then a random sample was chosen from each group.. DOOR PRIZES Each of. the participants in a conference was given a numbered name tag. Twenty-five numbers were chosen at random to receive a door prize.. a group of readers of a magazine; all readers of the magazine; biased; voluntary response COLLEGE For Exercises 22 and 23, use the following information. The graph at the right reveals that 56% of survey respondents did not have a formal financial plan for a child’s college tuition.. b. Classify the sample as simple, stratified, or systematic. Since the numbers were chosen randomly, this is a simple random sample because each participant was equally likely to be chosen.. Exercises. 2. GARDENING A gardener divided a lot into 25-square-foot sections. He then took 2 soil samples from each and tested the samples for mineral content. 2 soil. samples from each section; entire lot; stratified. in the class; simple 3. SCHOOL One hundred students in the lunch room are chosen for a survey. All students in the school eat lunch at the same time. 100 students; all. a group of employees; all employees of the company; unbiased; stratified 21. MOVIES A magazine is trying to determine the most popular actor of the year. It asks its readers to mail the name of their favorite actor to the magazine’s office.. a. Identify the sample and suggest a population from which it was chosen. The sample was 25 participants of the conference. The population was all of the participants of the conference.. Identify each sample, suggest a population from which it was selected, and classify the sample as simple, stratified, or systematic. 1. SCHOOL Each student in a class of 25 students was given a number at the beginning of the year. Periodically, the teacher chooses 4 numbers at random to display their homework on the overhead projector. 4 students; 25 students. 20. BUSINESS To get reaction about a benefits package, a company uses a computer program to randomly pick one person from each of its departments. Lesson 13-1. Simple Random Sample. 4. SHOPPING Every tenth person leaving a grocery store was asked if they would participate in a community survey. every. tenth person leaving a grocery store; all shoppers at the grocery store; systematic. students; simple. NAME ______________________________________________ DATE. ____________ PERIOD _____. Skills Practice, p. 783 and 13-1 Practice (Average) Practice, p. Bias 784 (shown) Sampling and. Identify each sample, suggest a population from which it was selected, and state whether it is unbiased (random) or biased. If unbiased, classify the sample as simple, stratified, or systematic. If biased, classify as convenience or voluntary response. 1. GOVERNMENT At a town council meeting, the chair asks 5 citizens attending for their opinions on whether to approve rezoning for a residential area. 5 citizens of a town;. all citizens of a town; biased; convenience 2. BOTANY To determine the extent of leaf blight in the maple trees at a nature preserve, a botanist divides the reserve into 10 sections, randomly selects a 200-foot by 200-foot square in the section, and then examines all the maple trees in the section. the maple. trees in a square area of each of 10 sections at a nature preserve; all the maple trees at the nature preserve; unbiased; stratified 3. FINANCES To determine the popularity of online banking in the United States, a polling company sends a mail-in survey to 5000 adults to see if they bank online, and if they do, how many times they bank online each month. 5000 U.S. adults; all U.S.. ★ 22. 22. We know that the results are from a national survey ★ 23. conducted by Yankelovich Partners for Microsoft Corporation. 23. Additional information needed ★ 24. includes how the survey was conducted, how the survey respondents were ★ 25. selected, and the number of respondents. ★ 26.. 4. SHOES A shoe manufacturer wants to check the quality of its shoes. Every twenty minutes, 20 pairs of shoes are pulled off the assembly line for a thorough quality inspection. 20 pairs of shoes every 20 minutes on an assembly line; all the. 6. BUSINESS An insurance company checks every hundredth claim payment to ensure that claims have been processed correctly. every hundredth claim payment at an. insurance company; all claim payments at an insurance company; unbiased; systematic 7. ENVIRONMENT Suppose you want to know if a manufacturing plant is discharging contaminants into a local river. Describe an unbiased way in which you could check the river water for contaminants. Sample answer: At a different time each day,. take a 10-ounce sample of water from given locations just upstream and just downstream from where the plant discharges its wastes. Compare the samples for contaminants to see if any are entering the river from the discharge.. 27. Sample answer: ★ 27. Randomly pick 5 rows from each field of tomatoes and then pick a tomato every 50 ft along each row.. ELL. Read the introduction to Lesson 13-1 at the top of page 708 in your textbook. From what group are the CDs picked at random and then checked for defects? All of the CDs that are burned.. Suppose the principal at a school wants to use Saturdays as make-up days when school is closed for inclement weather. The principal selects and then polls a group of students to see if the student body supports the idea. Complete the sentences. from which a. sample. is selected to be polled. If all the students are polled, it is called a. 712. Chapter 13 Statistics. convenience sample. If the principal announces a poll and then interviews the students who sign up to be interviewed, then the sample is a sample.. 3. Numbers can be assigned to all students and a computer can select 50 of the numbers at random. The students assigned those numbers would be polled. This would be a. simple random sample. If students are first divided according to grade and then chosen at random from each group, then the sample is a. random. sample.. samples are unbiased since they are selected without preference. for one unit of the population over another. A or parts of the population over other parts.. biased. sample favors one part. NAME ______________________________________________ DATE. 13-1 Enrichment Enrichment,. ____________ PERIOD _____. p. 786. Geometric Vanishing Acts Puzzles of this type use a “trick” drawing. It appears that rearranging the pieces of each figure causes one or more squares to disappear. Make figures of your own on graph paper. Then explain the “trick” in each puzzle. 1. The rectangle has an area of 65 square units, but the square has an area of only 64 square units.. 2. The square has an area of 64 square units, but the rectangle has an area of only 63 square units. C. B. Helping You Remember. A. B. C. 5. To remember what a stratified random sample is, look up the word stratified in a dictionary. What everyday meaning do you find that seems closest to the mathematical meaning presented in this lesson? Sample answer: to become formed into layers. B B. C. D. A A. A C D. The triangle C actually has a height 1. 712. Chapter 13 Statistics. Plans. row. 49%. mor For To. 46%. ents ent Ev. Curr. Source: National Pork Producers Council. sample. If only those students who are in the four classrooms closest to the principal’s office are selected for the poll, then the sample is a. 4. All. 65% s. New lated. y-Re. FARMING Suppose you are a farmer and want to know if your tomato crop is ready to harvest. Describe an unbiased way to determine whether the crop is ready to harvest.. systematic random. stratified random. e. How th. Famil. .. 2. If all students are requested to enter school through the administration building and every twenty-fifth student is selected to be polled, then the sample is a. voluntary response. 73% as Day W. Study the proposal. Describe its strengths and weaknesses. Is the sample a stratified random sample? Explain. See margin.. of students. census. Sample answer: Get a copy of the list of registered voters in the city and call every 100th person. Topics at Family FAMILY Study the graph at the right. Dinners. Divide the student body according to those who are on the basketball team, those who are in the band, and those who are in the drama club. Then take a simple random sample from each of the three groups. Conduct the survey using this sample.. Reading the Lesson. population. ELECTIONS Suppose you are running for mayor of your city and want to know if you are likely to be elected. Describe an unbiased way to poll the voters.. 29. CRITICAL THINKING The following is a proposal for surveying a stratified random sample of the student body.. Why is sampling important in manufacturing?. 1. The student body is the. Sample answer: Get a copy of the school’s list of students and call every 10th person on the list.. Sample answer: Every hour pull one infant seat from the end of the assembly line for testing.. ____________ PERIOD _____. Reading 13-1 Readingto to Learn Learn Mathematics Mathematics, p. 785 Sampling and Bias. SCHOOL Suppose you want to sample the opinion of the students in your school about a new dress code. Describe an unbiased way to conduct your survey.. manufactured by your company meet the government standards for safety. Describe an unbiased way to determine whether the seats meet the standards.. answer: Obtain a list of all teachers at the school. Assign each teacher a number, and then randomly select 10 numbers. Interview each of the teachers assigned one of the selected numbers.. Pre-Activity. Source: Yankelovich Partners for Microsoft Corp.. ★ 28. MANUFACTURING Suppose you want to know whether the infant car seats. 8. SCHOOL Suppose you want to know the issues most important to teachers at your school. Describe an unbiased way in which you could conduct your survey. Sample. NAME ______________________________________________ DATE. 56%. Not Sure 3%. See margin.. pairs of shoes coming down an assembly line; unbiased; systematic. of a company; all employees of a company; unbiased; simple. What additional information would you like to have about the sample to determine whether the sample is biased?. A national survey asked U.S. parents: Do you have a formal financial plan or program that Yes will provide for 41% the future cost of your child’s education? No. Describe the information that is revealed in the graph. What information is there about the type or size of the sample?. adults; biased; voluntary response. 5. BUSINESS To learn which benefits employees at a large company think are most important, the management has a computer select 50 employees at random. The employees are then interviewed by the Human Relations department. 50 employees. Write a statement to describe what you do know about the sample.. Planning for Kids‘ College Costs.

(16) 30. WRITING IN MATH. Answer the question that was posed at the beginning of the lesson. See pp. 751A–751B.. 4 Assess. Why is sampling important in manufacturing? Include the following in your answer: • an unbiased way to pick which CDs to check, and • a biased way to pick which CDs to check.. Standardized Test Practice. Open-Ended Assessment. 31. To predict the candidate who will win the seat in city council, which method would give the newspaper the most accurate result? B A B C D. Ask every 5th person that passes a reporter in the mall. Use a list of registered voters and call every 20th person. Publish a survey and ask readers to reply. Ask reporters at the newspaper.. 32. A cookie manufacturer plans to make a new type of cookie and wants to know if people will buy these cookies. For accurate results, which method should they use? D A B C D. Ask visitors to their factory to evaluate the cookie. Place a sample of the new cookie with their other cookies, and ask people to answer a questionnaire about the cookie. Take samples to a school, and ask students to raise their hands if they like the cookie. Divide the United States into 6 regions. Then pick 3 cities in each region at random, and conduct a taste test in each of the 18 cities.. Maintain Your Skills Mixed Review. Solve each equation. (Lesson 12-9) 5 3 10 1 1 1 1 33. 3 34. 8 2y r4 3y 4 3 r r Simplify.. (Lesson 12-8). 5. 35. 2 x 6 36. x 5 x 3. 3 1 2m 35. 2 4m m3 25. a a 12 a5 37. a7 a 12. 6. 39. GEOMETRY What is the perimeter of 䉭ABC? (Lesson 11-2). 226 cm. t2 4 t2 5t 6. 1 38. t2 t3. 424 cm. 56 cm. Solve each equation by using the Quadratic Formula. Approximate any irrational roots to the nearest tenth. (Lesson 10-4) 40. x2 6x 40 0 4, 10 41. 6b2 15 19b 2 1 1, 1 3 2 Find each product. (Lesson 8-7). 42. 2d2 9d 3 0.3, 4.8. 43. (y 5)(y 7). 45. (x 4)(x 8). Getting Ready for the Next Lesson. 44. (c 3)(c 7). c 2 10c 21. x 2 4x 32. BASIC SKILL Find each sum or difference. 46. 4.5 3.8 8.3. 47. 16.9 7.21 24.11. 48. 3.6 18.5 22.1. 49. 7.6 3.8 3.8. 50. 18 4.7 13.3. 51. 13.2 0.75 12.45 Lesson 13-1 Sampling and Bias. Getting Ready for Lesson 13-2 BASIC SKILL Students will learn how to organize data in matrices, and how to add and subtract matrices in Lesson 13-2. It is important that students understand basic addition and subtraction in order to add and subtract matrices. Use Exercises 46–51 to determine your students’ familiarity with basic addition and subtraction.. Answer. 354 cm. y 2 12y 35. Speaking Pass out newspapers or news magazines and have students scan the articles for the results of opinion polls. When students find such results, have them identify the sample and population for the poll. Then have them describe how the people conducting the poll could make sure the sample was not biased.. 713. 29. It is a good idea to divide the school population into groups and to take a simple random sample from each group. The problem that prevents this from being a legitimate stratified random sample is the way the three groups are formed. The three groups probably do not represent all students. The students who do not participate in any of these three activities will not be represented in the survey. Other students may be involved in two or three of these activities. These students will be more likely to be chosen for the survey.. Answer 26. The graph shows four phrases with a percent associated with each phrase. We can assume that the percents indicate the percent of respondents who said the indicated topic was discussed during family dinners. Based on the sum of the percents, respondents must have been able to choose or state more than one topic. We do not know how many respondents there were, whether the respondents selected topics from a list of choices or stated their own topics, whether there were any restrictions that may have existed about the topics, and the time period of the family dinners considered in this survey (a night, a week, a month, or more). Lesson 13-1 Sampling and Bias 713.

(17) Reading Mathematics. Getting Started Before using this page, ask students if they have ever asked for permission from their parents to do something, and tried to influence the way their parents answered. Have volunteers describe some of the methods they use to influence their parents’ decisions.. Teach Biased Questions Discuss with students why the two questions about sales tax on Internet purchases might have elicited different responses. Explain that the reason for saying “yes” to question two is that the question points out that the tax would have been paid at a store purchase. People are more likely to agree to spending money that they would have otherwise spent elsewhere, so the question is biased.. Assess Study Notebook Ask students to summarize what they have learned about asking biased questions in their study notebooks.. ELL English Language Learners may benefit from writing key concepts from this activity in their Study Notebooks in their native language and then in English.. Answers 1a. This question will bias people toward answering “yes” because it gives them a reason to think that recycling will help alleviate a shortage in resources. 714. Chapter 13 Statistics. Survey Questions Even though taking a random sample eliminates bias or favoritism in the choice of a sample, questions may be worded to influence people’s thoughts in a desired direction. Two different surveys on Internet sales tax had different results. Question 1 Should there be sales tax on purchases made on the Internet?. Yes 38%. Don't know or refused to answer 10%. No 52%. Question 2 Do you think people should or should not be required to pay the same sales tax for purchases made over the Internet that they would if they had bought the item in person at a local store?. Yes 65% No 28%. Don't know or refused to answer 7%. Notice the difference in Questions 1 and 2. Question 2 includes more information. Pointing out that customers pay sales tax for items bought at a local store may give the people answering the survey a reason to answer “yes.” Asking the question in that way probably led people to answer the way they did. Because they are random samples, the results of both of these surveys are accurate. However, the results could be used in a misleading way by someone with an interest in the issue. For example, an Internet retailer would prefer to state the results of Question 1. Be sure to think about survey questions carefully to make sure that you interpret the results correctly.. Reading to Learn For Exercises 1– 2, tell whether each question is likely to bias the results. Explain your reasoning. 1–3. See margin. 1. On a survey on environmental issues: a. “Due to diminishing resources, should a law be made to require recycling?” b. “Should the government require citizens to participate in recycling efforts?” 2. On a survey on education: a. “Should schools fund extracurricular sports programs?” b. “The budget of the River Valley School District is short of funds. Should taxes be raised in order for the district to fund extracurricular sports programs?” 3. Suppose you want to determine whether to serve hamburgers or pizza at the class party. a. Write a survey question that would likely produce biased results. b. Write a survey question that would likely produce unbiased results. 714 Investigating Slope-Intercept Form 714 Chapter 13 Statistics. 1b. This question will bias people toward answering “no” because most citizens are against the government making laws that require certain behaviors. 2a. This question is not biased. It does not lead to a yes or no answer. 2b. This question will bias people toward answering “no” because most people do not want taxes to be raised.. 3a. Sample answer: Since we had hamburgers at the last party, would you prefer pizza for the next party? 3b. Sample answer: Would you prefer hamburgers or pizza for the class party?.

(18) Lesson Notes. Introduction to Matrices • Organize data in matrices.. 1 Focus. • Solve problems by adding or subtracting matrices or by multiplying by a scalar.. Vocabulary • • • • • •. are matrices used to organize data?. matrix dimensions row column element scalar multiplication. 5-Minute Check Transparency 13-2 Use as a quiz or review of Lesson 13-1.. To determine the best type of aircraft to use for certain flights, the management of an airline company considers the following aircraft operating statistics.. Aircraft. Number of Seats. Airborne Speed. Possible Flight Distance. Fuel per Hour. Operating Cost per Hour. (mph). (miles). (gallons). (dollars). B747-100. 462. 512. 2297. 3517. 7224. DC-10-10. 297. 496. 1402. 2311. 5703. MD-11. 259. 527. 3073. 2464. 6539. A300-600. 228. 475. 1372. 1505. 4783. Mathematical Background notes are available for this lesson on p. 706C.. Building on Prior Knowledge In Chapter 2, students learned how to add and subtract rational numbers using a number line. In this lesson, students will use this skill to add and subtract rational numbers in matrices.. Source: Air Transport Association of America. The table has rows and columns of information. When we concentrate only on the numerical information, we see an array with 4 rows and 5 columns.. . 462 297 259 228. 512 496 527 475. . 2297 3517 7224 1402 2311 5703 3073 2464 6539 1372 1505 4783. This array of numbers is called a matrix.. ORGANIZE DATA IN MATRICES If you have ever used a spreadsheet program on the computer, you have worked with matrices. A matrix is a rectangular arrangement of numbers in rows and columns. A matrix is usually described by its dimensions , or the number of rows and columns, with the number of rows stated first. Each entry in a matrix is called an element .. Example 1 Name Dimensions of Matrices State the dimensions of each matrix. Then identify the position of the circled element in each matrix. 2 4 a. [11 15 24] b. 1 0 3 6 This matrix has 1 row and 3 columns. Therefore, it is a This matrix has 3 rows and 1-by-3 matrix. 2 columns. Therefore, it is a 3-by-2 matrix. The circled element is in the first row and the second The circled element is in the column. third row and the first column.. . . Lesson 13-2 Introduction to Matrices. are matrices used to organize data? Ask students: • Which lines of numbers are the rows of the matrix? The rows go from left to right. • Which lines of numbers are the columns? The columns go from top to bottom. • In what instances might putting numerical data from a table into a matrix be beneficial? Sample answer: Putting numerical data into a matrix might make it easier to perform calculations on the data.. 715. Resource Manager Workbook and Reproducible Masters Chapter 13 Resource Masters • Study Guide and Intervention, pp. 787–788 • Skills Practice, p. 789 • Practice, p. 790 • Reading to Learn Mathematics, p. 791 • Enrichment, p. 792 • Assessment, p. 825. Graphing Calculator and Spreadsheet Masters, p. 47 Parent and Student Study Guide Workbook, p. 102. Transparencies 5-Minute Check Transparency 13-2 Answer Key Transparencies. Technology Interactive Chalkboard. Lesson x-x Lesson Title 715.

(19) Two matrices are equal only if they have the same dimensions and each element of one matrix is equal to the corresponding element in the other matrix.. 2 Teach. 13 54 13 54. ORGANIZE DATA IN MATRICES. In-Class Example. 3 7 4 2 4 7 ,B , and C 4 1 6 3 6 0 If the sum does not exist, write impossible. If A . 13. a. A B. 12 3 by 1; a.  7  5 second row, first column. AB.  2 8 14 1 b.  6 3 2 12 5 19  22 15 3 by 4; first row, fourth column.  2 6  13 7 a. 8 11  9 4  10 5 7 12  15 13  1 15  3 17 3 8 1 12 6 b. 14 3 6 1  7 20 40. . 4 6. 7 7 0 1. 13 71. . 100. b. B C. College Football Each year the National Football Foundation awards the MacArthur Bowl to the number one college football team. The bowl is made of about 400 ounces of silver and represents a stadium with rows of seats.. 71. . . 4 2 6 3. . . . 6 , find each sum. 5. Substitution. 4 (4) 7 (2) 6 6 0 (3). . 5 8 12 3. . Definition of matrix addition. Simplify.. 3 4 2 4 6 3. . 6 5. . Substitution. Addition and subtraction of matrices can be used to solve real-world problems.. Example 3 Subtract Matrices COLLEGE FOOTBALL The Division I-A college football teams with the five best records during the 1990s are listed below.. Source: ESPN Information Please® Sports Almanac. Florida State Nebraska Marshall Florida Tennessee. Overall Record Wins Losses Ties 1 13 109 1 16 108 0 25 114 1 22 102 2 22 99. . . Bowl Record Wins Losses Ties Florida State 0 2 8 Nebraska 0 5 5 Marshall 0 1 2 Florida 0 4 5 Tennessee 0 4 6. . . . 101 11 1 103 11 1 112 24 0 97 18 1 93 18 2. . . 716 Chapter 13 Statistics. Interactive. Chalkboard PowerPoint® Presentations. Chapter 13 Statistics. . Use subtraction of matrices to determine the regular season records of these teams during the decade. 109 8 13 2 1 0 8 2 0 109 13 1 108 5 16 5 1 0 5 5 0 108 16 1 114 25 0 2 1 0 114 2 25 1 0 0 102 5 22 4 1 0 5 4 0 102 22 1 99 6 22 4 2 0 6 4 0 99 22 2. impossible. 716. . 8 0 3 0. Since B is a 2-by-3 matrix and C is a 2-by-2 matrix, the matrices do not have the same dimensions. Therefore, it is impossible to add these matrices.. MATRIX OPERATIONS. does not exist, write impossible.. 13. . . BC. 2 Find each sum. If the sum. . 8 4 3 1. Example 2 Add Matrices. matrix. Then identify the position of the circled element in each matrix.. Power Point®. 41. MATRIX OPERATIONS If two matrices have the same dimensions, you can add or subtract them. To do this, add or subtract corresponding elements of the two matrices.. Power Point®. 1 State the dimensions of each. In-Class Example. 21 47 21 37. This CD-ROM is a customizable Microsoft® PowerPoint® presentation that includes: • Step-by-step, dynamic solutions of each In-Class Example from the Teacher Wraparound Edition • Additional, Your Turn exercises for each example • The 5-Minute Check Transparencies • Hot links to Glencoe Online Study Tools.

(20) So, the regular season records of the teams can be described as follows. Regular Season Record Wins Losses Ties Florida State 101 1 11 Nebraska 1 11 103 Marshall 0 24 112 Florida 1 18 97 Tennessee 2 18 93. . In-Class Examples. Power Point®. Teaching Tip. Explain that in this example, the overall record includes the regular season record, plus the bowl (postseason) record.. . 3 COLLEGE FOOTBALL The You can multiply any matrix by a constant called a scalar. This is called scalar multiplication. When scalar multiplication is performed, each element is multiplied by the scalar and a new matrix is formed.. Division 1-A current football coaches with the five best overall records as of 2000 are listed below. Overall Record. Scalar Multiplication of a Matrix. . . . a b c ma mb mc m d e f md me mf. Example 4 Perform Scalar Multiplication 2 4 1 , find 3T. 0 3 6. . If T . . 2 4 3T 3 1 0 3 6 . . Concept Check 1. A 2-by-4 matrix has 2 rows and 4 columns, and a 4-by-2 matrix has 4 rows and 2 columns.. Definition of scalar multiplication. 6 12 3 0 9 18. Simplify.. 3 4 7 4 4. Won Lost Tied 20 17 11 8 4. 9 6 8 6 6. 1 1 2 0 0. Use subtraction of matrices to determine the regular season records of these coaches.. See margin.. 01. 4 1. 3. FIND THE ERROR Hiroshi and Estrella are finding 5. Hiroshi 3. 90 87 110 93 104. Source: NCAA. 2. OPEN ENDED Write two matrices whose sum is. –1. 322 315 224 172 147. Joe Paterno Bobby Bowden Lou Holtz Jackie Sherrill Ken Hatfield. 1. Describe the difference between a 2-by-4 matrix and a 4-by-2 matrix.. –5. Joe Paterno Bobby Bowden Lou Holtz Jackie Sherrill Ken Hatfield. Bowl Record. 3(2) 3(4) 3(1) 3(0) 3(3) 3(6). . Won Lost Tied. Coach. Substitution. . Coach. 5 4. 3 . 9. . 3 . 1 2 5. Estrella 5 3. –2 5 = 10 5. –5. –2. . –1 3 5 = 5 10. –15 –25. . Regular Season Record Coach Won Lost Tied Joe Paterno 302 81 2 Bobby Bowden 298 81 3 Lou Holtz 213 102 5 Jackie Sherrill 164 87 4 Ken Hatfield 143 98 4. 8 4 If R  5 12 3 , find 5R. 25 40  60 15. Who is correct? Explain your reasoning. Estrella; Hiroshi did not multiply each. www.algebra1.com/extra_examples. Answer 2. Sample answer:. 2 3 1 3 2 1 6 6 5 6 2 5 4 7 6 14. element of the matrix by 5.. Lesson 13-2 Introduction to Matrices 717. FIND THE ERROR Have students identify the difference between the two results first, which will help them pinpoint the error.. Lesson 13-2 Introduction to Matrices 717.

(21) Guided Practice. 3 Practice/Apply. GUIDED PRACTICE KEY Exercises. Examples. 4–7 8–11 12–16. 1 2–4 3. Study Notebook Have students— • add the definitions/examples of the vocabulary terms to their Vocabulary Builder worksheets for Chapter 13. • include explanations on how to identify the properties of matrices, and how to perform matrix operations. • include any other item(s) that they find helpful in mastering the skills in this lesson.. About the Exercises… Organization by Objective • Organize Data in Matrices: 17–26, 39, 42, 45, 46 • Matrix Operations: 27–38, 40, 41, 43, 44, 47, 48 Odd/Even Assignments Exercises 17–38 are structured so that students practice the same concepts whether they are assigned odd or even problems. Alert! Exercises 53–57 require students to use graphing calculators.. Assignment Guide Basic: 17–23 odd, 27–33 odd, 39–41, 49–52, 58–70 Average: 17–37 odd, 39–44, 49–52, 58–70 (optional: 53–57) Advanced: 18–38 even, 42–68 (optional: 69, 70) All: Practice Quiz 1 (1–5). State the dimensions of each matrix. Then, identify the position of the circled element in each matrix. 2 0 4 5. [3 3 1 9] 1 by 4; first row, 4. 5 1 3 3 by 3; first row, first column 7 second column 2 6. . . 5 2 6. 1 3. 5 22. 24 13. . 20 12. . Chapter 13 Statistics. . by 2; first row, 3second column. 4.2 0.6 1.7 1.05 0.625 2.1. . . 24. 10. 2A 40. 12. 12 F 11 14. 10 8 8. 3 8 10. 13 R 1 8. 12 5 11. 11 10 2. 11 N 1 10. 8 8 15. 6 11 11. . 20 38. . 28]. 11. 4C [20. PIZZA SALES For Exercises 12–16, use the following tables that list the number of pizzas sold at Sylvia’s Pizza one weekend. FRIDAY. Small. Medium. Thin Crust. 12. 10. Large 3. Thick Crust. 11. 8. 8. Deep Dish. 14. 8. 10. SATURDAY. Small. Medium. Large. Thin Crust. 13. 12. 11. Thick Crust. 1. 5. 10. Deep Dish. 8. 11. 2 Large. SUNDAY. Small. Medium. Thin Crust. 11. 8. 6. Thick Crust. 1. 8. 11. Deep Dish. 10. 15. 11. 12. Create a matrix for each day’s data. Name the matrices F, R, and N, respectively.. 14. 36 30 20 13. Does F equal R? Explain. No; the corresponding elements are not equal. T 13 21 29 14. Create matrix T to represent F R N. 32 34 23 15. What does T represent? the total sales for the weekend 16. small, thin crust 16. Which type of pizza had the most sales during the entire weekend? pizza ★ indicates increased difficulty. Practice and Apply Homework Help For Exercises. See Examples. 17–26 27–38 39–48. 1 2–4 3. State the dimensions of each matrix. Then, identify the position of the circled element in each matrix. 17–24. See margin. 1 3 36 3 56 21 2 1 17. 18. 19. 20. 0 25 1 60 112 65 5 8 1 11 14. . Extra Practice See page 849.. 718. 21.. . . 4 5 6. . 0 1 3. 2 12 7. . 22.. . 1 3 1 1. 2 4 5 7. . 23.. 54. . 3 0. . 1 2. 24.. Chapter 13 Statistics. Answers 17. 2 by 2; first row, first column 18. 3 by 2; second row, first column 19. 3 by 1; third row, first column 20. 2 by 3; second row, second column. 718. 7.. 8. A C impossible 9. B A. Application. . 4 by 1; third row, first column. 10 15 14 ,B , and C [5 7], find each sum, difference, or 19 10 6 product. If the sum or difference does not exist, write impossible.. If A . 9.. . 21. 3 by 3; second row, third column 22. 4 by 2; fourth row, first column 23. 2 by 3; second row, third column 24. 2 by 2; second row, first column. 65. . . 3 4.

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