Pre-Algebra A survey asked 22 students how many hours of TV they watched daily. The results are shown. Display the data in a frequency table. Then make a line plot. Lesson Frequency Tables, Line Plots, and Histograms Additional Examples NumberTallyFrequency List the numbers of hours in order Count the tally marks and record the frequency Use a tally mark for each result. ||| |||| | |||| ||

Pre-Algebra Twenty-one judges were asked how many cases they were trying on Monday. The frequency table below shows their responses. Display the data in a line plot. Then find the range. Lesson 12-1 “How many cases are you trying?” NumberFrequency Frequency Tables, Line Plots, and Histograms Additional Examples

Pre-Algebra (continued) Lesson 12-1 The greatest value in the data set is 4 and the least value is 0. So the range is 4 – 0, or 4. For a line plot, follow these steps 1, 2, and 3. 3 Write a title that describes the data. Cases Tried by Judges 2 Mark an x for each response.x xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx 1 Draw a number line with the choices below it Frequency Tables, Line Plots, and Histograms Additional Examples

Pre-Algebra Box-and-Whisker Plots The data below represent the wingspans in centimeters of captured birds. Make a box-and-whisker plot Lesson 12-2 Additional Examples Step 1:Arrange the data in order from least to greatest. Find the median Step 2:Find the lower quartile and upper quartile, which are the medians of the lower and upper halves lower quartile = 28 upper quartile = 61

Pre-Algebra Step 3: Draw a number line. Mark the least and greatest values, the median, and the quartiles. Draw a box from the first to the third quartiles. Mark the median with a vertical segment. Draw whiskers from the box to the least and greatest values. Box-and-Whisker Plots Lesson 12-2 (continued) Additional Examples

Pre-Algebra Draw a number line for both sets of data. Use the range of data points to choose a scale. Draw the second box-and-whisker plot below the first one. Box-and-Whisker Plots Use box-and-whisker plots to compare test scores from two math classes. Lesson 12-2 Class A: 92, 84, 76, 68, 90, 67, 82, 71, 79, 85, 79 Class B: 78, 93, 81, 98, 69, 95, 74, 87, 81, 75, 83 Additional Examples

Pre-Algebra Box-and-Whisker Plots Describe the data in the box-and-whisker plot. Lesson 12-2 The lowest score is 55 and the highest is 85. Half of the scores are at or between 66 and 80 and thus within 10 points of the median, 76. One fourth of the scores are at or below 66 and one fourth of the scores are at or above 80. Additional Examples

Pre-Algebra Box-and-Whisker Plots The plots below compare the percents of students who were eligible to those who participated in extracurricular activities in one school from 1992 to What conclusions can you draw? Lesson 12-2 About 95% of the students were eligible to participate in extracurricular activities. Around 60% of the students did participate. A little less than two thirds of the eligible students participated in extracurricular activities. Additional Examples

Pre-Algebra Using Graphs to Persuade Which title would be more appropriate for the graph below: “Texas Overwhelms California” or “Areas of California and Texas”? Explain. Lesson 12-3 Additional Examples

Pre-Algebra Using Graphs to Persuade (continued) Lesson 12-3 Because of the break in the vertical axis, the bar for Texas appears to be more than six times the height of the bar for California. Actually, the area of Texas is about 267,000 mi 2, which is not even two times the area of California, which is about 159,000 mi 2. The title “Texas Overwhelms California” could be misleading. “Areas of Texas and California” better describes the information in the graph. Additional Examples

Pre-Algebra Using Graphs to Persuade Study the graphs below. Which graph gives the impression of a sharper increase in rainfall from March to April? Explain. Lesson 12-3 Additional Examples

Pre-Algebra Using Graphs to Persuade (continued) Lesson 12-3 In the second graph, the months are closer together and the rainfall amounts are farther apart than in the first graph. Thus the line appears to climb more rapidly from March to April in the second graph. Additional Examples

Pre-Algebra Using Graphs to Persuade What makes the graph misleading? Explain. Lesson 12-3 The “cake” on the right has much more than two times the area of the cake on the left. Additional Examples

Pre-Algebra Counting Outcomes and Theoretical Probability The school cafeteria sells sandwiches for which you can choose one item from each of the following categories: two breads (wheat or white), two meats (ham or turkey), and two condiments (mayonnaise or mustard). Draw a tree diagram to find the number of sandwich choices. Lesson 12-4 There are 8 possible sandwich choices. mayonnaise Each branch of the “tree” represents one choice—for example, wheat-ham- mayonnaise. wheat white ham turkey ham turkey mayonnaise mustard mayonnaise mustard mayonnaise mustard Additional Examples

Pre-Algebra Counting Outcomes and Theoretical Probability How many two-digit numbers can be formed for which the first digit is odd and the second digit is even? Lesson 12-4 There are 25 possible two-digit numbers in which the first digit is odd and the second digit is even. 55=25 first digit, possible choices second digit, possible choices numbers, possible choices Additional Examples

Pre-Algebra Counting Outcomes and Theoretical Probability Use a tree diagram to show the sample space for guessing right or wrong on two true-false questions. Then find the probability of guessing correctly on both questions. Lesson 12-4 The tree diagram shows there are four possible outcomes, one of which is guessing correctly on both questions. P(event) = Use the probability formula. number of favorable outcomes number of possible outcomes The probability of guessing correctly on two true/false questions is right wrong right wrong = 1414 Additional Examples

Pre-Algebra Counting Outcomes and Theoretical Probability In some state lotteries, the winning number is made up of five digits chosen at random. Suppose a player buys 5 tickets with different numbers. What is the probability that the player has a winning number? Lesson 12-4 First find the number of possible outcomes. For each digit, there are 10 possible outcomes, 0 through 9. 1st digit outcomes 10 2nd digit outcomes 10 3rd digit outcomes 10 5th digit outcomes 10 4th digit outcomes 10 total outcomes = 100,000 Then find the probability when there are five favorable outcomes. P(winning number) = = number of favorable outcomes number of possible outcomes 5 100, ,000 The probability is, or. 1 20,000 Additional Examples

Pre-Algebra Independent and Dependent Events Lesson 12-5 You roll a number cube once. Then you roll it again. What is the probability that you get 5 on the first roll and a number less than 4 on the second roll? The probability of rolling 5 and then a number less than 4 is P(5, then less than 4) = P(5) P(less than 4) = =, or P(5) = 1616 There is one 5 among 6 numbers on a number cube. P(less than 4) = 3636 There are three numbers less than 4 on a number cube. Additional Examples

Pre-Algebra Independent and Dependent Events Bluebonnets grow wild in the southwestern United States. Under the best conditions in the wild, each bluebonnet seed has a 20% probability of growing. Suppose you plant bluebonnet seeds in your garden and use a fertilizer that increases to 50% the probability that a seed will grow. If you select two seeds at random, what is the probability that both will grow in your garden? Lesson 12-5 P(two seeds grow) = P(a seed grows) P(a seed grows) The probability that two seeds will grow is 25%. P(a seed grows) = 50%, or 0.50Write the percent as a decimal. = Substitute. = 0.25 Multiply. = 25% Write 0.25 as a percent. Additional Examples

Pre-Algebra Independent and Dependent Events Three girls and two boys volunteer to represent their class at a school assembly. The teacher selects one name and then another from a bag containing the five students’ names. What is the probability that both representatives will be boys? Lesson 12-5 P(boy, then boy) = P(boy) P(boy after boy) The probability that both representatives will be boys is =, or Simplify. = Substitute. P(boy after boy) = 1414 If a boy’s name is drawn, one of the four remaining students is a boy. P(boy) = 2525 Two of five students are boys. Additional Examples

Pre-Algebra Permutations and Combinations Find the number of permutations possible for the letters H, O, M, E, and S. Lesson st letter 5 choices 5 2nd letter 4 choices 4 3rd letter 3 choices 3 5th letter 1 choice 1 4th letter 2 choices 2= 120 There are 120 permutations of the letters H, O, M, E, and S. Additional Examples

Pre-Algebra Permutations and Combinations In how many ways can you line up 3 students chosen from 7 students for a photograph? Lesson students Choose 3. 7 P 3 = = 210Simplify You can line up 3 students from 7 in 210 ways. Additional Examples

Pre-Algebra Permutations and Combinations In how many ways can you choose two states from the table when you write reports about the areas of states? Lesson 12-6 State Area (mi 2 ) Alabama Colorado Maine Oregon Texas 50, ,729 30,865 96, ,914 Make an organized list of all the combinations. Additional Examples

Pre-Algebra Permutations and Combinations (continued) Lesson 12-6 AL, CO AL, ME AL, OR AL, TXUse abbreviations of each CO, ME CO, OR CO, TXstate’s name. First, list all ME, OR ME, TXpairs containing Alabama. OR, TXContinue until every pair of states is listed. There are ten ways to choose two states from a list of five. Additional Examples

Pre-Algebra Permutations and Combinations How many different pizzas can you make if you can choose exactly 5 toppings from 9 that are available? Lesson toppings Choose 5. 9 C 5 = 9P55P59P55P5 You can make 126 different pizzas. = = 126 Simplify Additional Examples

Pre-Algebra Permutations and Combinations Tell which type of arrangement—permutations or combinations—each problem involves. Explain. Lesson 12-6 a. How many different groups of three vegetables could you choose from six different vegetables? b. In how many different orders can you play 4 DVDs? Combinations; the order of the vegetables selected does not matter. Permutations; the order in which you play the DVDs matters. Additional Examples

Pre-Algebra Experimental Probability A medical study tests a new medicine on 3,500 people. It produces side effects for 1,715 people. Find the experimental probability that the medicine will cause side effects. Lesson 12-7 The experimental probability that the medicine will cause side effects is 0.49, or 49%. P(event)= number of times an event occurs number of times an experiment is done = = ,715 3,500 Additional Examples

Pre-Algebra Experimental Probability Simulate the correct guessing of answers on a multiple-choice test where each problem has four answer choices (A, B, C, and D). Lesson 12-7 Use a 4-section spinner to simulate each guess. Mark the sections as 1, 2, 3, and 4. Let “1” represent a correct choice. P(event)= = = number of times an event occurs number of times an experiment is done Here are the results of 50 trials The experimental probability of guessing correctly is Additional Examples

Pre-Algebra Random Samples and Surveys You want to find out how many people in the community use computers on a daily basis. Tell whether each survey plan describes a good sample. Explain. Lesson 12-8 a. Interview every tenth person leaving a computer store. b. Interview people at random at the shopping center. c. Interview every tenth student who arrives at school on a school bus. This is not a good sample. People leaving a computer store are more likely to own computers. This is a good sample. It is selected at random from the population you want to study. This is not a good sample. This sample will be composed primarily of students, but the population you are investigating is the whole community. Additional Examples

Pre-Algebra Random Samples and Surveys From 20,000 calculators produced, a manufacturer takes a random sample of 300 calculators. The sample has 2 defective calculators. Estimate the total number of defective calculators. Lesson 12-8 Estimate: About 133 calculators are defective. defective sample calculators sample calculators defective calculators calculators = Write a proportion n 20,000 = Substitute. 2(20,000) = 300n Write cross products. 2(20,000) n 300 = Divide each side by n Simplify. Additional Examples

Pre-Algebra A softball player has an average of getting a base hit 2 times in every 7 times at bat. What is an experimental probability that she will get a base hit the next time she is at bat? Lesson 12-9 You can use a spinner to simulate the problem. Construct a spinner with seven congruent sections. Make five of the sections blue and two of them red. The blue sections represent not getting a base hit and the red sections represent getting a base hit. Each spin represents one time at bat. Problem Solving Strategy: Simulate the Problem Additional Examples

Pre-Algebra (continued) Lesson 12-9 Use the results given in the table below. “B” stands for blue and “R” stands for red. BBBBRRBBRBBRBBRBBBBRRBBRBBBBRBBBBBBBBBBBBBRBBBRBBBBBBRRBBBBRRBBBBBBBBBBBBBBBRRBBBRRBBRBBBBBBBBBRBBBRBBBBRRBBRBBRBBRBBBBRRBBRBBBBRBBBBBBBBBBBBBRBBBRBBBBBBRRBBBBRRBBBBBBBBBBBBBBBRRBBBRRBBRBBBBBBBBBRBBBR Problem Solving Strategy: Simulate the Problem Additional Examples

Pre-Algebra (continued) Lesson 12-9 Make a frequency table. An experimental probability that she gets a base hit the next time she is at bat is 0.22, or 22%. Makes a Base Hit Doesn’t Make a Base Hit |||| |||| |||| |||| |||||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| ||| Problem Solving Strategy: Simulate the Problem Additional Examples