Practice Mean, Median, Mode, and Range. Find the mean, median, mode, and range of each data set , 35, 23, 37, 29, 53, 43

Transcription

1 Chapter 12 Practice 12-1 Mean, Median, Mode, and Range Find the mean, median, mode, and range of each data set , 35, 23, 37, 29, 53, , 56, 47, 69, 75, 48, 56, , 11, 80, 19, 27, 19, 10, 25, , 8, 20, 6, 9, 11, 10, 8, 9, 8 5. The line plot shows the number of hours 15 students said they spent on homework in one week. Which measure of central tendency best describes the data? Justify your answer. Identify the outlier in the data set. Then determine how the outlier affects the mean, median, and mode of the data , 16, 13, 15, 5, 16, 12

2 Name Date Class Identify the outlier in the data set. Then determine how the outlier affects the mean, median, and mode of the data. 7. 7, 7, 4, 9, 6, 26, 4, 5, 8, 4 Determine and find the most appropriate measure of central tendency or range for each situation. Refer to the table at the right for Exercises Which measure best describes the middle of the data? 9. Which earthquake magnitude occurred most frequently? 10. How spread out are the data? Some Major Earthquakes in United States History Year Location Magnitude 1812 Missouri California California Alaska Alaska Alaska Idaho Alaska Alaska California A restaurant offers 3 meals at $12 each, 8 meals at $8 each, and 6 meals at $7 each. Calculate the weighted average price per meal, to the nearest cent. (Hint: Multiply each price by the corresponding number of meals. Then divide by the total number of meals.)

3 Grade pg. 58

4 Grade pg. 59

5 Chapter 12-2 Practice 12-2 Box-and-Whisker Plots 1. Use the data to make a box-and-whisker plot. 19, 46, 37, 16, 24, 47, 23, 19, 31, 25, 42 Use the box-and-whisker plot of games won per season by the New York Yankees and the Arizona Diamondbacks for for Exercises Which team has the greater median number of games won? 3. Which team has the greater interquartile range of games won? 4. Which team appears to have a more predictable performance? Use the box-and-whisker plot of nightly tip totals that a waitress gets at two different restaurants for Exercises At which restaurant is the median tip total greater? 6. At which restaurant is the interquartile range of tip totals greater? 7. At which restaurant does the tip total appear to be more predictable?

6 Use the data for Exercises , 42, 26, 32, 40, 28, 36, 27, 29, 6, Make two box-and-whisker plots of the data on the same number line: one plot with the outlier and one plot without the outlier. 9. How does the outlier affect the interquartile range of the data? 10. Which is affected more by the outlier: the range or the interquartile range? The table shows scores for two golfers. Use the table for Exercises 4 7. Henry Trish Make two box-and-whisker plots of the data on the same number line. 12. Which golfer has the lower median score? 13. Which golfer has the lesser interquartile range of scores? 14. Which golfer appears to be more consistent?

7 Chapter 12 Practice 12-3 Populations and Samples 1. Determine which sampling method will better represent the entire population. Justify your answer. Reading Habits of High School Students Sampling Method Dinah surveys 48 students who she knows. Suki gives survey forms to 100 students who were randomly chosen from a school attendance list. Results of Survey 91% have read a novel in the past month. 59% have read a novel in the past month. For Problems 2 and 3, determine whether each sample may be biased. Explain. 2. An on-line bookseller randomly chooses 200 book buyers from its database and then surveys those book buyers to find out if they were satisfied with the time it took to deliver their orders. 3. Milena surveys 80 high school students who are leaving a jazz concert to determine the favorite type of music among high school students. 4. Zack chooses a random sample of 50 out of 400 students. He finds that 7 of them have traveled to a foreign country. Zack claims that over 50 of the 400 students have traveled to a foreign country. Do you agree? Explain your answer. 5. A mint produces 150,000 souvenir coins each year. In a random sample of 400 coins, 3 have a misprint. Predict the number of coins that will have misprints in a year.

8 6. Determine which sampling method will better represent the entire population. Justify your answer. The Midland Company: Employee Satisfaction Sampling Method Wanda interviews 80 employees who were randomly selected from the company payroll list. Bernard interviews the last 30 employees to be hired. Results of Survey 69% feel adequately challenged by their jobs 90% feel adequately challenged by their jobs. For Problems 2 and 3, determine whether each sample may be biased. Explain. 7. A landlord s 60 of his 1,250 tenants and surveys them to determine whether they would like to use the Internet to pay rent. 8. An insurance company surveys 350 of its customers by randomly choosing names from its customer database and then telephoning the customers. Explain whether you would survey the entire population or use a sample. 9. You want to know how many hours members of a sports team train each week during the off-season. 10. You want to know the average income of people who eat at vegetarian restaurants across the country.

9 Chapter 12 Practice 12-4 Probability These are the results of the last math test. The teacher determines that anyone with a grade of more than 70 passed the test. Give the probability for the indicated grade. Grade # of Students P(70) 2. P(100) 3. P(80) 4. P(passing) 5. P(grade 80) 6. P(60) 7. P(failing) 8. P(grade 80) A bowling game consists of rolling a ball and knocking up to 5 pins down. The number of pins knocked down are then counted. The table gives the probability of each outcome. Number of Pins Down Probability What is the probability of knocking down all 5 pins? 10. What is the probability of knocking down no pins? 11. What is the probability of knocking down at most 2 pins?

10 12. Four friends are playing a game. Jordan has a 45% chance of winning. Diane is twice as likely to win than Carlos, while Stacey has a 25% chance. Create a table of probabilities for the sample space. Outcome Probability Use the spinner to determine the probability of each outcome. 13. P(white 1) 14. P(dots 2) 15. P(lines even) 16. P(dots 1) 17. P(white odd) 18. P(dots integer) 19. P(odd) 20. P(white or 2) 21. There are six teams competing to collect the most food for the food bank. Team B has a 30% chance of winning. Teams A, C, D, and E all have the same chance of winning. Team F is one-third as likely to win as Team B. Create a table of probabilities for the sample space. Outcome Probability

11 Chapter 12 Practice 12-5 Experimental Probability 1. A movie theater sells popcorn in small, medium, large and jumbo sizes. The customers of the first show purchase 4 small, 20 medium, 40 large, and 16 jumbo containers of popcorn. Estimate the probability of the purchase of a medium container of popcorn. 2. Melissa was able to make 6 free throws out of her last 10 attempts. Estimate the probability that she will hit the next free throw. 3. The table shows the different bus routes available to the residents of a city. Estimate the probability that a resident will take Route A. Bus Route Route A Route B Route C Route D Residents Which DJ has the highest probability that a song played will be classical? DJ Song lists DJ Classical Songs Number of Songs Thomas Guy Paul

12 5. The developer of a Web page wants to track the number of hits to each link of the Web page. An automatic counter records the following hits in one week: home, 60 hits; FAQ, 20 hits; employment opportunities, 15 hits; products, 50 hits; order status, 30 hits; and contact information, 25 hits. Estimate the probability of a hit on the contact information page. The table shows how many times a song on a CD was played at a party. Song Frequency Estimate the probability for each of the following. 6. P(song 2) 7. P(song 4) 8. P(song 5) 9. P(song 8) 10. P(song 9) 11. P(song 13) 12. Use the table to compare the probability that Song 10 was played to the probability that Song 6 was played. 13. About 1 in 6 students will get a brain teaser correct. Based on this probability, approximately how many will get be correct, if 53 students are asked the brain teaser?

13 Chapter 12 Practice 12-6 Sample Spaces 1. Marcus spins the spinner at the right and flips a dime at the same time. What are the possible outcomes? How many outcomes are in the sample space? 2. For lunch, Britney has a choice of a hot dog, a hamburger, or pizza and a choice of an apple, a pear, or grapes. What are all the possible choices of lunch she can have? How many outcomes are in the sample space? 3. Susan and Ryan are playing a game that involves spinning the spinner at the right and flipping a penny. How many outcomes are possible in the game? 4. An Italian restaurant offers small, medium, and large calzones. The choices of fillings are cheese, sausage, spinach, or vegetable. How many different calzones can you order? 5. There are 5 ways to go from Town X to Town Y. There are 3 ways to go from Town Y to Town Z. How many different ways are there to go from Town X to Town Z, passing through Town Y? 6. Rasheed has tan pants, black pants, gray pants, and blue pants. He has a brown sweater and a white sweater. How many different ways can he wear a sweater and pants together?

14 1. Joanna spins the spinners at the right at the same time. What are the possible outcomes? How many outcomes are in the sample space? 2. For breakfast, Armando has a choice of pancakes, eggs, or cereal and a choice of milk, hot cocoa, or juice. What are all the possible choices of breakfast he can have? How many outcomes are in the sample space? 3. Shannon and Tyler are playing a game that involves spinning the spinner shown at the right and tossing a 1 6 number cube. How many outcomes are possible in the game? 4. If you flip a penny, toss a 1 6 number cube, and flip a quarter, how many outcomes are possible? 5. A Chinese restaurant has a special on Friday nights. For $20, you can choose one dish from 6 choices in column A and one dish from 5 choices in Column B. In addition, you can choose egg drop or wonton soup. How many different specials can you order? 6. Lisa has a beige skirt, a black skirt, and a denim skirt. She has a red sweater and a white sweater, and she has a white blouse, a blue blouse, and a green blouse. How many different ways can she wear a skirt, sweater, and blouse together?

15 Chapter 12 Practice 12-7 Theoretical Probability An experiment consists of rolling one fair number cube. Find the probability of each event. 1. P(3) 2. P(7) 3. P(1 or 4) 5. P( 5) 7. P(2 or odd) 4. P(not 5) 6. P( 4) 8. P( 3) An experiment consists of rolling two fair number cubes. Find the probability of each event. 9. P(total shown 3) 10. P(total shown 7) 11. P(total shown 9) 12. P(total shown 2) 13. P(total shown 4) 14. P(total shown 13) 15. P(total shown 8) 16. P(total shown 12) 17. P(total shown 7) 18. Find the probability that a point chosen randomly inside the triangle is within the square. Round to the nearest hundredth. (area of square = s 2, area of triangle =.5bh) 19. In a game two fair number cubes are rolled. To make the first move, you need to roll a total of 6, 7, or 8. What is the probability that you will be able to make the first move?

16 An experiment consists of rolling two fair number cubes. Find the probability of each event. 20. P(total shown 5) 21. P(total shown 3) 22. P(total shown 10) 24. P(total shown 7) Three separate jars each contain 2 different color marbles. Jar A has a red and a blue marble. Jar B has a red and a green marble. Jar C has a purple and a white marble. One marble is drawn from each jar. The table shows a sample space with all outcomes equally likely. Find each probability. 26. P(RRP) 27. P(BGW) 23. P(total shown 12) 25. P(total shown 4) Jar A Jar B Jar C Outcome R R P RRP R R W RRW R G P RGP R G W RGW B R P BRP B R W BRW B G P BGP B G W BGW 28. P(2 red with another 29. P(a green with two 30. P(1 white or 1 purple) color) other colors) 31. Find the probability that a point chosen randomly inside the circle is within the triangle. Round to the nearest hundredth. (area of triangle =.5bh, area of circle = 3.14r 2 ) 32. In a game two fair number cubes are rolled. To make the first move, you need to roll a total of 7, 8, or 9. What is the probability that you will be able to make the first move?

17 Seventh Grade 2004 pg. 46

18 Seventh Grade 2004 pg. 47

19 Seventh Grade 2003 pg. 48

20 Seventh Grade 2003 pg. 49

21 Chapter 12 Practice 12-8 Making Predictions Make a prediction based on an experimental probability. 1. A baseball player reaches base 35% of the time. How many times can he expect to reach base in 850 at-bats? 3. In 1951, Odessa, Texas had temperatures of at least 95 F 11% of the time. During that year, how many days could residents predict would have highs of at least 95 F? 2. Annette, Alaska, gets about 30% as much rain as Barrow, Alaska, which gets rain 4% of the time. In a year (365 days), how many days can residents of Annette expect it to rain? 5. A hockey goalie blocks 89% of shots at the goal. How many shots can the goalie predict she or he will block in 758 tries? 4. Going door to door, Lil has educated 93% of the people in her town about recycling. If she has the same rate of success for 5,400 houses, how many people will she reach? Make a prediction based on a theoretical probability. 7. Gil rolls a number cube 78 times. How many times can he expect to roll an odd number greater than 1? 8. Jenna flips two pennies 105 times. How many times can she expect both coins to come up heads? 9. A shoebox holds same-size disks. There are 5 red, 6 white, and 7 blue disks. You pick out a disk, record its color, and return it to the box. If you repeat this process 250 times, how many times can you expect to pick either a red or white disk? 10. Ron draws 16 cards from a standard deck of 52. The deck is made up of equal numbers of four suits clubs, diamonds, hearts, and spades. How many of the cards drawn can Ron expect to be spades?

22 Solve each problem. 11. During February and March, Jack is spending 7 days in the Yukon to check on endangered species. The region has snowfall that blocks roads 20 days during these months. Can Jack expect to be able to get around at least 5 of the days? Explain. 12. Ted plans a 21-day skiing vacation in December through February. The area he is considering is open 46 days during this period. Ted would like at least 14 days of skiing. Will this area meet his needs? Explain 13. Airline 1 loses passengers luggage 4.1% of the time, Airline 2 loses luggage 4 times in 95. Which airline has a better record? Explain. 14. ABC Airlines has had delays on 18 of 126 recent flights. DEF Airlines has had delays 13% of the time. Which airline would you expect to provide more reliable service? Why? Make a prediction based on a theoretical probability. 15. A bag has 7 blue marbles, 3 red, 4 green, and 8 white. You pick a marble, record its color, and return it. If you repeat this process 665 times, how many times can you expect to pick a blue or green marble? 16. A bag holds nine $1 bills, seven $5 bills, and two $10 bills. You pick a bill, record the denomination, and return it. In 438 repetitions, how many times can you expect to pick $5? 17. Shari rolls a pair of number cubes, numbered 1 to 6, 64 times. How many times can she expect to roll an odd number? 18. A spinner has 12 equal sections 5 red, 4 green, and the rest black. In 921 spins, how many times can you expect to spin black?

23 Chapter 12 Practice 12-9 Independent and Dependent Events Determine if the events are dependent or independent. 1. choosing a tie and shirt from the closet 2. choosing a month and tossing a coin 3. rolling two fair number cubes once, then rolling them again if you received the same number on both number cubes on the first roll An experiment consists of rolling a fair number cube and tossing a fair coin. 4. Find the probability of getting a 5 on the number cube and tails on the dime. 5. Find the probability of getting an even number on the number cube and heads on the dime. 6. Find the probability of getting a 2 or 3 on the number cube and heads on the dime. A box contains 3 red marbles, 6 blue marbles, and 1 white marble. The marbles are selected at random, one at a time, and are not replaced. Find the probability. 7. P(blue and red) 8. P(white and blue) 9. P(red and white) 10. P(red and white and 11. P(red and red and 12. P(red and blue and blue) blue) blue) 13. P(red and red and 14. P(white and blue 15. P(white and red red) and blue) and white)

24 Consider a regular deck of cards without the jokers. Cards are replaced after each draw. Find the probability of each of the following. 16. P(pair of red kings) 17. P(a diamond and a black seven) Use the same deck of cards but do not replace the card after each draw. 18. P(ace of hearts and king of hearts) 19. P(a ten and a jack) 20. P(red card and a black card) 21. P(a club and king or red ace) 22. Mr. and Mrs. Reginald are expecting their first baby. The doctor tells them they are having triplets. What is the probability that the babies will all be the same sex? 23. Sid has a bag of 12 red, 14 brown, and 10 blue marbles. He chooses one, shoots it, and chooses another. What is the probability that his first selection is a red marble, and then a blue marble? 24. If Justine s initials are JMD, what is the probability that she will draw her initials from a box containing the letters of the alphabet? There is no replacement of letters after each is drawn. 25. There are 13 math students, 10 science students, and 17 English students in a group. If only one prize is allowed per person, what is the probability that the moderator will award a science student a prize and then award another prize to a math student?

25 Chapter 12 Lesson The Fundamental Counting Principle Employee identification codes at a company contain 2 letters followed by 2 numbers. All codes are equally likely. 1. Find the number of possible identification codes. 2. Find the probability of being assigned the code MT Find the probability that an ID code of the company does not contain the letter A as the second letter of the code. 4. Find the probability that an ID code of the company does not contain the number Mrs. Sharpe is planning her dinners for next week. The choices for the entree are roast beef, turkey, or pork. The choices of carbohydrates are mashed potatoes, baked potatoes, or noodles. The vegetable choices are broccoli, spinach, or carrots. Make a tree diagram indicating the possible outcomes for each entree. 6. How many different meals could Mrs. Sharpe prepare?

26 Find the probability for each of the following. 7. P(dinner with baked potato) 8. P(dinner with noodles and carrots) 9. There are 10 gloves in a drawer, 6 leather and 4 cotton. Two gloves are drawn. What is the probability the gloves match?

27 Chapter 12 Lesson Combinations and Permutations 1. A chef has some broccoli, cauliflower, carrots, and squash to make a vegetarian dish. List the possible combinations if he uses only 3 vegetables in the dish. 2. Lauren, Manuel, Nick, Opal, and Pat are forming groups of two to work on a drama production. List the different combinations of students that are possible using the first initial of each name. 3. On Sundays at Ice Cream Heaven, you can choose two free toppings for your sundae. The toppings are nuts, hot fudge, caramel, and sprinkles. How many different combinations of toppings can you order? 4. The students in Mrs. Mandel s class need to choose two class representatives from six nominated students. How many different combinations of class representatives are possible? 5. How many two-person carpools are possible with seven people?

28 6. Joe has homework assignments for math, Spanish, and history. In how many different orders can he do his homework? 7. Find the number of permutations of the letters in the word SMART. 8. In how many ways can you arrange the numbers 6, 7, 8, and 9 to make a four-digit number? 9. Nine mountain bikers are on a bicycle trip. In how many possible ways can they follow each other? 10. How many permutations of the letters A through F are there? 11. Ed, Martine, Sal, Carl, Paula, Terry, Ken, Leo, Ursula, and Jamie are in a race. In how many different orders can they finish? 12. Melinda has 15 art trophies. Write an expression that shows how many different ways she can line up her trophies on a shelf.