Unit 4. Statistics, Data Analysis, and Probability. Use statistical measures and probability to describe data.

Transcription

1 Unit 4 Statistics, Data Analysis, and Probability Use statistical measures and probability to describe data. CHAPTER 8 Statistics: Analyzing Data Use measures of central tendency and range to describe a set of data. Create and read graphs that depict data. CHAPTER 9 Probability Students use probability and proportions to make predictions. 392 James Richard/Stock Connection/PictureQuest

2 in Science Math Genes What s math have to do with genetics? Well, you re about to find out. You ll research basic genetics and learn how to use a Punnett square. Then you ll create sample genes for pet traits. You ll make predictions based on the pets traits to determine the traits of their offspring. So, put on your lab coat and grab your math tool kit to begin this adventure. IL Math Online Log on to glencoe.com to begin. Unit 4 Statistics, Data Analysis, and Probability 393

3 8 Statistics: Analyzing Data Illinois Learning Standards 1.A.3a Construct, read and interpret tables, graphs (including circle graphs) and charts to organize and represent data. 1.A.3b Compare the mean, median, mode and range, with and without the use of technology. Key Vocabulary histogram (p. 416) measures of central tendency (p. 42) range (p. 397) scatter plot (p. 427) Real-World Link Amusement Parks Hershey Park in Pennsylvania has over 6 rides and attractions. You can use a bar graph to display and then compare the speeds of these rides. Statistics: Analyzing Data Make this Foldable to help you organize your notes. Begin with nine sheets of notebook paper. 1 Fold 9 sheets of paper in half along the width. 2 Cut a 1 tab along the left edge through one thickness. 3 Glue the 1 tab down. Write the lesson number and title on the front tab. 4 Repeat Steps 2 and 3 for the remaining sheets. Staple them together on the glued tabs to form a booklet. 8-1 Line Plots 394 Chapter 8 Statistics: Analyzing Data

4 GET READY for Chapter 8 Diagnose Readiness You have two options for checking Prerequisite Skills. Option 1 Option 2 Take the Quick Quiz below. Refer to the Quick Review for help. IL Math Online Take the Online Readiness Quiz at glencoe.com. Order from least to greatest. (Lesson 4-9) , 96.2, , 5.62, , 22, JEANS A store sells boot-cut jeans for $49.97, classic for $49.79, and flared for $ Write these prices in order from least to greatest. (Lesson 4-9) Example 1 Order 47.7, 47.7, and 4.7 from least to greatest Line up the decimal points 47.7 and compare place value. 4.7 The numbers in order from least to greatest are 4.7, 47.7, and Order from greatest to least. (Lesson 4-9) , 74.67, , 1.26, , 3.4, 3.34 Example 2 Order 2.8, 2.8,.28 from greatest to least. 2.8 Line up the decimal points 2.8 and compare place value..28 The numbers in order from greatest to least are 2.8, 2.8, and.28. Evaluate each expression. (Lesson 1-4) PIZZA Four friends ordered a large pizza for $14.95, a salad for $3.75, and two bottles of soda for $2.25 each. If they split the cost evenly, how much does each person owe? (Lesson 1-4) Example Evaluate = _ 11.7 Add 3.4, 4.5, and = 3.9 Divide 11.7 by 3. Chapter 8 Get Ready for Chapter 8 395

5 8-1 Line Plots MAIN IDEA Display and analyze data using a line plot. IL Learning Standards 1.A.3a Construct, read and interpret tables, graphs (including circle graphs) and charts to organize and represent data. New Vocabulary statistics data line plot outlier cluster range analyze IL Math Online glencoe.com Concepts In Motion Extra Examples Personal Tutor Self-Check Quiz Reading in the Content Area BUILDINGS The table shows the number of stories in 2 of the tallest buildings in Boston, Massachusetts. 1. Do any of the values seem much greater or much less than the other data values? 2. Do some of the buildings have the same height? Is this easy to see? Explain. Boston s Tallest Buildings (Number of Stories) Source: Emporis Buildings Statistics deals with collecting, organizing, and interpreting data. Data are pieces of information, which are often numerical. One way to show how data are spread out is to use a line plot. A line plot is a diagram that shows the data on a number line. Display Data Using a Line Plot 1 BUILDINGS Make a line plot of the data shown above. Step 1 Step 2 Draw a number line. The shortest building in the table has 26 stories, and the tallest has 6. You can use a scale of 25 to 65 and an interval of 5. Other scales and intervals could also be used Put an above the number that represents the number of stories in each building. Include a title a. BUILDINGS The number of stories in the 15 tallest buildings in the world are listed at the right. Display the data in a line plot. World s Tallest Buildings (Number of Stories) Source: The World Almanac 396 Chapter 8 Statistics: Analyzing Data

6 You can make some observations about the distribution of data, or how data are grouped together or spread out. Consider the line plot below. Outlier data that are separated from rest of data Cluster data that are grouped closely together another outlier Vocabulary Link Range Everyday Meaning in music, all the notes between the high and low notes, as in a singer with a wide range. Math Use the difference between the greatest number and least number in a set of data. In a line plot, you can easily find the range, or spread, of the data, which is the difference between the greatest and least numbers. When you analyze data, you use these observations to describe and compare data. Use a Plot to Analyze Data 2 ANIMALS The line plot below shows the life spans for different animals. Identify any clusters, gaps, and outliers and find the range Clusters You can describe a cluster by stating a range of values or by giving a single value around which the data appear to be grouped. Many of the data cluster between 1 and 12 years. There is a gap between 25 and 4 years. Since 4 is apart from the rest of the data, it is an outlier. The greatest age is 4 years, and the least age is 6 years. So, the range of the ages is 4-6 or Describe how the range would change if the data value 54 was added to the data set in Example 2. The greatest age would change to 54, and the least age would remain the same at 6. So, the range of the ages would change from 34 to 54-6 or 48. Refer to Example 1. b. Identify any clusters, gaps, and outliers and find the range. c. Describe how the range would change if the data value 5 was added to the data set. Lesson 8-1 Line Plots 397

7 Example 1 (p. 396) Display each set of data in a line plot. 1. Costs of Video Games ($) Sizes of Tennis Shoes MUSIC For Exercises 3 and 4, analyze the line plot below. Number of Music CDs Owned Example 2 (p. 397) Example 3 (p. 397) Example 2 (p. 397) Example 3 (p. 397) 3. Identify any clusters, gaps, and outliers and find the range of the data. 4. Describe how the range would change if the data value 3 was added to the data set. SURVEYS For Exercises 5 8, analyze the line plot at the right and use the information below. Jamie asked her classmates how many glasses of water they drink on a typical day. The results are shown. 5. What was the most frequent response? 6. What was the least frequent response? 7. What is the range? Glasses of Water Consumed Describe how the range would change if an additional data value of 4 was added to the data set. HOMEWORK HELP For Exercises HELP See Examples Display each set of data in a line plot. 9. Snowfall (in.) Drink Size (oz) Basketball Scores (points) Ages of Students (y) Chapter 8 Statistics: Analyzing Data

8 WEATHER For Exercises 13 16, analyze the line plot that shows the record high temperatures recorded by weather stations in each of the fifty states. Record High Temperatures ( F) Real-World Link Death Valley National Park is the site of the highest temperature ever recorded in the United States, 134 F. Source: Death Valley Chamber of Commerce Source: The World Almanac 13. What is the range of the data? 14. What temperature occurred most often? 15. Identify any clusters, gaps, or outliers. 16. Describe how the range of the data would change if 134 F were not part of the data set. MOVIES For Exercises 17 2, analyze the line plot below that shows the number of digital video discs various students have in their DVD collection. Digital Video Disc (DVD) Collection 17. Find the range of the data What number of DVDs occurred most often? 19. How many students have more than 15 DVDs in their collection? 2. Describe how the range would change if the data value 38 was added to the data set. Determine whether each statement is sometimes, always, or never true. Explain your reasoning. 21. If a new piece of data is added to a data set, the range will change. 22. If there is a cluster, it will appear in the center of the line plot. BOOKS For Exercises 23 25, analyze the line plot at the right. 23. How many students read 4 or more books? 24. How many more students read 1 2 books than 5 6 books? Number of Books Read About what percent of the students read less than 5 books? Lesson 8-1 Line Plots 399

9 GOVERNMENT For Exercises 26 28, refer to the table showing the number of representatives for each of the Northeast states. The House of Representatives Northeast States State Number CT 5 DE 1 ME 2 MD 8 State Number MA 1 NH 2 NJ 13 NY 29 State Number PA 19 RI 2 VT Display the data in a line plot. 27. Find the range and determine any clusters, gaps, or outliers. 28. Use the line plot to summarize the data. 29. The number of House of Representatives for the ten Southwestern states is quite different. The Southwestern states have 4, 8, 53, 7, 7, 3, 3, 5, 32, and 3 representatives. Display this data in a line plot. Compare this line plot to the line plot you made in Exercise 26. Include a discussion about clusters, outliers, range, and gaps in data. ILS ISAT Extra Practice, pp. 687, COLLECT THE DATA Conduct a survey of your classmates to determine how many hours of television they watch on a typical school night. Then display and analyze the data in a line plot. Use your analysis of the data to write a convincing argument about television viewing on a school night. H.O.T. Problems 31. REASONING Explain how the inclusion or exclusion of outliers affects the computation of the range of a data set. 32. FIND THE ERROR Elena and Rashaun are analyzing the data shown in the line plot at the right. Who is correct? Explain greatest data value: 2 least data value: 1 Elena greatest data value: 16 least data value: 1 Rashaun 33. CHALLENGE Compare and contrast line plots and frequency tables. Include a discussion about what they show and when it is better to use each one. 4 Chapter 8 Statistics: Analyzing Data

10 WRITING IN 34. MATH The number of fundraising items sold by two grades is shown. Describe which grade is more consistent and explain how you know. Fundraising Items Fundraising Items Seventh Grade Eighth Grade ISAT PRACTICE 1.A.3a 35. The graph shows the weight of the emperor penguins at a zoo. Emperor Penguins Weight (kg) Which statement is not valid? A More than half of these penguins weigh at least 41 kilograms. B There are 16 emperor penguins at the zoo. C Of these penguins, 3% weigh between 3 and 38 kilograms. D The range of the emperor penguins weight is or 26 kilograms. 36. The table shows the math scores for 24 students in Mr. Baker s class. Math Test Scores How would the range of the test scores change if a score of 83 was added? F The range would remain unchanged at 45. G The range would remain unchanged at 35. H The range would change from 45 to 83. J The range would change from 35 to 17. Find the interest earned to the nearest cent for each principal, interest rate, and time. (Lesson 7-8) 37. $3, 1%, 2 years 38. $9, 5.5%, 4.5 years 39. BASEBALL CARDS What is the total cost of a package of baseball cards if the regular price is $4.19 and the sales tax is 6.5%? (Lesson 7-7) 4. Solve m + 18 = 33 mentally. (Lesson 1-7) PREREQUISITE SKILL Add or divide. Round to the nearest tenth if necessary _ 44. _ Lesson 8-1 Line Plots 41

11 8-2 Measures of Central Tendency and Range MAIN IDEA Describe a set of data using mean, median, mode, and range. The number of pennies in each cup represents Jack s scores for five math quizzes. IL Learning Standards 1.A.3a Construct, read and interpret tables, graphs (including circle graphs) and charts to organize and represent data. 1.A.3b Compare the mean, median, mode and range, with and without the use of technology. New Vocabulary measures of central tendency mean median mode 6 1 Move the pennies among the cups so that each cup has the same number of pennies. 1. What was Jack s average score for the five quizzes? 2. If Jack scores 14 points on the next quiz, how many pennies would be in each cup? A number used to describe the center of a set of data is a measure of central tendency. The most common of these measures is the mean. Mean Words Key Concept The mean of a set of data is the sum of the data divided by the number of items in the data set. The mean is also referred to as average. IL Math Online glencoe.com Extra Examples Personal Tutor Self-Check Quiz Examples data set: 1 cm, 1 cm, 5 cm, 2 cm, 2 cm, 4 cm, 2 cm, 5 cm mean: or 2.75 cm 8 Find the Mean 1 QUIZ SCORES The table shows the quiz scores Quiz Scores for 16 students. Find the mean mean = =_ or sum of data number of data items a. MONEY Adam earned $14, $1, $12, $15, and $13 by doing chores around the house. What is the mean amount Adam earned doing these chores? 42 Chapter 8 Statistics: Analyzing Data

12 Two other common measures of central tendency are median and mode. Median Key Concept Vocabulary Link Median Everyday Use the middle paved or planted section of a highway, as in median strip. Math Use the middle number of the ordered data. Words Example Mode Words Example In a data set that has been ordered from least to greatest, the median is the middle number if there is an odd number of data items. If there is an even number of data items, the median is the mean of the two numbers closest to the middle. data set: 7 yd, 11 yd, 15 yd, 17 yd, 2 yd, 2 yd median: _ or 16 yd 2 The median divides the data in half. The mode of a set of data is the number that occurs most often. If there are two or more numbers that occur most often, all of them are modes. data set: 5 mi, 45 mi, 45 mi, 52 mi, 49 mi, 56 mi, 56 mi modes: 45 mi and 56 mi Find the Mean, Median, and Mode 2 MOVIE RENTALS The number of DVDs rented during one week at Star Struck Movie Rental is shown in the table. What are the mean, median, and mode of the data? Star Struck Movie Rental Daily DVD Rentals S M T W TH F S mean: = _ 399 or median: 34, 34, 35, 55, 57, 78, 16 First, write the data in order. median mode: 34 It is the only value that occurs more than once. The mean is 57 DVDs, the median is 55 DVDs, and the mode is 34 DVDs. b. BICYCLES The sizes of the bicycles owned by the students in Ms. Garcia s class are listed in the table. What are the mean, median, and mode of the data? Students Bicycle Sizes (in.) c. FOOTBALL The points scored in each game by Darby Middle School s football team for 9 games are 21, 35, 14, 17, 28, 14, 7, 21, and 14. Find the mean, median, and mode. Lesson 8-2 Measures of Central Tendency and Range 43

13 ISAT EXAMPLE 1.A.3a, 1.A.3b 3 The maximum length in feet of several whales is listed below. Comparing Measures Another way to solve Example 3 is to find the measures before 98 is added to the data set. Then find the measures after 98 is added to the data set. Then compare. 46, 53, 33, 53, 79 If the maximum length of the Blue Whale, 98 feet, is added to this list, which of the following statements would be true? A The mode would decrease. C The mean would increase. B The median would decrease. D The mean would decrease. Read the Item You are asked to identify which statement would be true if the data value 98 was added to the data set. Solve the Item Use number sense to eliminate possibilities. The mode, 53, will remain unchanged since the new data value occurs only once. So, eliminate answer choice A. Since the new data value is greater than each value in the data set, the median will not decrease. So, eliminate answer choice B. The remaining two answer choices refer to the mean. Since 98 is greater than each value in the data set, the mean will increase, not decrease. So, the answer is C. d. If the maximum length of the Orca Whale, 3 feet, is added to the list in Example 3, which of the following statements would be true? F The mode would decrease. H The mean would increase. G The median would increase. J The mean would decrease. In addition to the mean, median, and mode, you can also use the range to describe a set of data. Below are some guidelines for using these measures. Mean, Median, Mode, and Range Concept Summary Measure Mean Median Mode Range Most Useful When... data set has no outliers data set has outliers there are no big gaps in the middle of the data data set has many identical numbers describing the spread of the data 44 Chapter 8 Statistics: Analyzing Data

14 4 PLANTS The line plot shows the height of desert cacti. Would the mean, median, mode, or range best represent the heights? mean: 14 7th term + 8th term median: 2 mode: 5 range: 3-1 or 29 Choose Mean, Median, Mode, or Range Median When there is an odd number of data, the median is the middle number of the ordered set. When there is an even number of data, the median is the mean of the two middle numbers or 8.8 = _ or 5 2 The mean of 8.8 misrepresents the score. The median or mode represents the height of the cacti well. e. GAMES The table shows the cost of various board games. Would the mean, median, mode, or range best represent the costs? Explain. Board Game Costs ($) Examples 1, 2 (pp ) Example 3 (p. 44) Find the mean, median, and mode for each set of data. Round to the nearest tenth if necessary. 1. Miles traveled on the weekend: 29, 14, 8, 59, 78, 3, 59, 69, 55, 5 2. Team Number of Wins Eagles 1 Hawks 8 Zipps 9 Falcons MULTIPLE CHOICE During the week, the daily low temperatures were 52 F, 45 F, 51 F, 45 F, and 48 F. If Saturday s low temperature of 51 F is added, which statement about the data set would be true? A The mean would decrease. C The mode would increase. B The median would decrease. D The mode would decrease Example 4 (p. 45) 5. SHOES The line plot shows the price of athletic shoes. Which measure best describes the data: mean, median, mode, or range? Explain Lesson 8-2 Measures of Central Tendency and Range 45

15 HOMEWORK HELP For Exercises HELP See Examples 1, Find the mean, median, and mode for each set of data. Round to the nearest tenth if necessary. 6. Number of dogs groomed each week: 65, 56, 57, 75, 76, 66, Daily number of boats in a harbor: 93, 84, 8, 91, 94, 9, 78, 93, 8 8. Scores earned on a math test: 95, 9, 92, 94, 91, 9, 98, 88, 89, 1 9. Prices of books: $1, $18, $11, $6, $6, $5, $1, $11, $46, $7, $6, $8 1. Cost Number of Coats $75 8 $8 3 $ MUSIC The line plot shows the number of weeks that songs have been on the Top 2 Country Songs list. Would the mean, median, mode, or range best represent the data? Explain. Country Songs Number of Weeks in Top SPACE Twenty-seven countries have sent people into space. The table shows the number of individuals from each country. Which measure best describes the data: mean, median, mode, or range? Explain. Real-World Link The International Space Station measures 356 feet by 29 feet, and contains almost an acre of solar panels. Source: The World Almanac People in Space Source: The World Almanac Find the mean, median, and mode for each set of data. Round to the nearest tenth if necessary. 14. Weight in ounces of various insects: 6.1, 5.2, 7.2, 7.2, 3.6, 9., 6.5, 7.4, Prices of magazines: $3.5, $3.75, $3.5, $4., $3., $3.5, $ Daily low temperatures: -2 F, -8 F, -2 F, F, -1 F, 1 F, -2 F, -1 F REASONING Determine whether each statement is always, sometimes, or never true about the data set {8, 12, 15, 23}. Explain your reasoning. 17. If a value greater than 23 is added, the mean will increase. 18. If a value less than or equal to 8 is added, the mean will decrease. 19. If a value between 8 and 23 is added, the mean will remain unchanged. 46 Chapter 8 Statistics: Analyzing Data CORBIS

16 DINOSAURS For Exercises 2 22, use the lengths of the dinosaurs shown below. Tyrannosaurus Rex Length: 48 inches Corythosaurus Length: 396 inches Parasaurolophus Length: 48 inches 2. What is the mean length of the dinosaurs? 21. One of the largest dinosaurs ever is the Brachiosaurus. Its length was 96 inches. If this data value is added to the lengths of the dinosaurs above, how will it affect the mean? Explain your reasoning. 22. Which measure best describes the data if the length of the Brachiosaurus is included: mean, median, mode, or range? If the length of the Brachiosaurus is not included? Explain any similarities or differences. 23. SPORTS The table shows the points scored by a lacrosse team so far this season. The team will play 14 games this season. How many points need to be scored during the last game so that the average number of points scored this season is 12? Explain. ILS ISAT Extra Practice, pp. 687, 711 H.O.T. Problems Hawks Lacrosse Team Points Scored FIND THE DATA Refer to the Data File on pages Choose some data and then describe it using the mean, median, mode, and range. 25. OPEN ENDED Give an example of a set of data in which the mean is not the best representation of the data set. Explain why not. 26. Which One Doesn t Belong? Identify the term that does not have the same characteristic as the other three. Explain your reasoning. mean median range mode 27. REASONING Determine whether the median is sometimes, always, or never part of the data set. Explain your reasoning. 28. CHALLENGE Without calculating, would the mean, median, or mode be most affected by eliminating 1, from the data shown? Which would be the least affected? Explain your reasoning. 5, 1, 75, 6, 75, 1,, 9, WR ITING IN MATH According to the U.S. Census Bureau, the typical number of family members per household is State whether this measure is a mean or mode. Explain how you know. Lesson 8-2 Measures of Central Tendency and Range 47

17 ISAT PRACTICE 1.A.3a, 1.A.3b 3. The table below shows the number of soup labels collected in one week by each homeroom in grade 7. Classroom Number of Soup Labels Mr. Martin 138 Ms. Davis 125 Mr. Cardona 89 Mrs. Turner 11 Mr. Wilhelm 13 Mrs. LaBash? Which number could be added to the set of data in order for the mode and median of the set to be equal? A 89 C 125 B 11 D An antique dealer purchased 5 antiques for a total of $85.. He later bought another antique for $758.. What is the mean cost of all the antiques? F $151.6 H $268. G $17. J $ Gina found the mean and median of the following list of numbers. 5, 7, 7 If the number 11 was added to this list, which of the following statements would be true? A The mean would increase. B The mean would decrease. C The median would increase. D The median would decrease. 33. TEMPERATURE The table shows record high temperatures for Kentucky in July. Make a line plot of the data. (Lesson 8-1) Find the simple interest earned to the nearest cent for each principal, interest rate, and time. (Lesson 7-8) 34. $1,25, 3.5%, 2 years 35. $569, 5.5%, 4 months July Temperatures FOOD The United States produced almost 11 Uses of Apples in the United States billion pounds of apples in a recent year. Use the information in the graph to find how many pounds of apples were used to make juice and cider. (Lesson 7-1) 37. Name the property shown by the statement 4 6 = 6 4. (Lesson 1-8) Juice and Cider 23% Canned Fruit 11% Other 7% Source: U.S. Apple Association Fresh Fruit 59% PREREQUISITE SKILL Name the place value of the underlined digit. (p. 669) , , Chapter 8 Statistics: Analyzing Data

18 Extend 8-2 Graphing Calculator Lab Mean and Median MAIN IDEA Use technology to calculate the mean and median of a set of data. IL Learning Standards 1.A.3b Compare the mean, median, mode and range, with and without the use of technology. You can more efficiently calculate the mean and median of a large set of data using a graphing calculator. COMPUTERS Kendrick surveys thirty seventh graders and asks them how many times they had to wait longer than 5 minutes during the previous week to use a computer in the school library. The results are shown below. Number of Times a Student Had to Wait to Use the Library Computer Find the mean and median of the data. Clear list L1 by pressing Enter the number of times students had to wait in L1. Press Display a list of statistics for the data by pressing 1. The first value, x, is the mean. Use the down arrow key to locate Med. The mean number of times a student waited was 3 and the median number of times was 2. ANALYZE THE RESULTS WRITING IN 1. MATH Kendrick claims that, on average, students had to wait more than 5 minutes about 3 times last week. Based on your own analysis of the data, write a convincing argument to dispute his claim. (Hint: Create and use a line plot of the data to support your argument.) 2. COLLECT THE DATA Collect some numerical data from your classmates. Then use a graphing calculator to calculate the mean and median of the data. After analyzing the data, write a convincing argument to support a claim you can make about your data. Extend 8-2 Graphing Calculator Lab: Mean and Median 49

19 8-3 Stem-and-Leaf Plots MAIN IDEA Display and analyze data in a stem-and-leaf plot. IL Learning Standards 1.A.3a Construct, read and interpret tables, graphs (including circle graphs) and charts to organize and represent data. 1.A.3b Compare the mean, median, mode and range, with and without the use of technology. New Vocabulary stem-and-leaf plot leaf stem IL Math Online glencoe.com Extra Examples Personal Tutor Self-Check Quiz BIRDS The table shows the average chick weight in grams of sixteen different species of birds. 1. Which chick weight is the lightest? 2. How many of the weights are less than 1 grams? Chick Weight (g) In a stem-and-leaf plot, the data are organized from least to greatest. The digits of the least place value usually form the leaves, and the next place-value digits form the stems. Display Data in a Stem-and-Leaf Plot 1 BIRDS Display the data in the table above in a stem-and-leaf plot. Step 1 Choose the stems using digits in the tens place,, 1, and 2. The least value, 5, has in the tens place. The greatest value, 25, has 2 in the tens place. Step 2 List the stems from least to greatest Stem Leaf in the Stem column. Write the leaves, the ones digits to the right of the corresponding stems Step 3 Order the leaves and write a key that explains how to read the stems and leaves. Include a title. The tens digits of the data form the stems. Chick Weight (g) Stem Leaf = 12 g Always write each leaf, even if it repeats. The ones digits of the data form the leaves. Include a key. a. HOMEWORK The number of minutes Homework Time (min) the students in Mr. Blackwell s class spent doing their homework one night is shown. Display the data in a stem-and-leaf plot Chapter 8 Statistics: Analyzing Data

20 Stem-and-leaf plots are useful in analyzing data because you can see all the data values, including the greatest, least, mode, and median value. Describe Data 2 CHESS The stem-and-leaf plot shows the Chess Matches Won number of chess matches won by Stem members of the Avery Middle School Chess Team. Find the range, median, and mode of the data. range: greatest wins - least wins = 61-8 or 53 median: middle value, or 35 wins mode: most frequent value, 4 Leaf = 32 wins b. BIRDS Find the range, median, and mode of the data in Example 1. Effect of Outliers Real-World Career How Does a Sports Scout Use Math? Sports scouts review game records and statistics and evaluate athletes skills. IL Math Online For more information, go to glencoe.com. 3 SPORTS The stem-and-leaf plot Basketball Points shows the number of points Stem scored by a college basketball player. Which measure of central tendency is most affected by the outlier? The mode, 26, is not affected by the inclusion of the outlier, 2. Leaf = 12 points Calculate the mean and median each without the outlier, 2. Then calculate them including the outlier and compare. mean: without the outlier median: including the outlier = The mean decreased by , or 1.2, while the median decreased by 23-22, or 1. Since 1.2 > 1, the mean is most affected. c. CHESS Refer to Example 2. If an additional student had 84 wins, which measure of central tendency would be most affected? Lesson 8-3 Stem-and-Leaf Plots 411

21 Example 1 (p. 41) Display each set of data in a stem-and-leaf plot. 1. Height of Trees (ft) 2. Cost of Shoes ($) Examples 2, 3 (p. 411) CAMP The stem-and-leaf plot at the right shows the ages of students in a pottery class. 3. What is the range of the ages of the students? 4. Find the median and mode of the data. 5. If an additional student was 6 years old, which measure of central tendency would be most affected? Ages of Students Stem Leaf = 1 years HOMEWORK HELP For Exercises 6 9 1, 11, 13, 14, , 15, 19 HELP See Examples Display each set of data in a stem-and-leaf plot. 6. Quiz Scores (%) 7. Low Temperatures ( F) Floats at Annual Parade School Play Attendance CYCLING The number of Tour de France titles won by eleven countries is shown. 1. Find the range of titles won. 11. Find the median and mode of the data. 12. Which measure of central tendency is most affected by the outlier? ELECTRONICS For Exercises 13 15, use the stem-and-leaf plot that shows the costs of various DVD players at an electronics store. 13. What is the range of the prices? 14. Find the median and mode of the data. 15. If an additional DVD player cost $153, which measure of central tendency would be most affected? Tour de France Titles Won by Eleven Countries Stem Leaf = 4 titles Costs of DVD Players Stem Leaf = $ Chapter 8 Statistics: Analyzing Data

22 HISTORY For Exercises 16 19, refer to the stem-and-leaf plot below. Ages of Signers of Declaration of Independence Stem Leaf = 31 years Real-World Link The saltwater crocodile is the largest living reptile. Some measuring 27 3 feet in length have been recorded in the wild. Source: PBS ILS ISAT Extra Practice, pp. 688, How many people signed the Declaration of Independence? 17. What was the age of the youngest signer? 18. What is the range of the ages of the signers? 19. Based on the data, can you conclude that the majority of the signers were 3 49 years old? Explain your reasoning. 2. GYMNASTICS The scores for 1 girls in a gymnastics event are 9.3, 1., 9.9, 8.9, 8.7, 9., 8.7, 8.5, 8.8, 9.3. Analyze a stem-and-leaf plot of the data to draw two conclusions about the scores. 21. REPTILES The average lengths of certain species of crocodiles are given in the table. Analyze a stem-and-leaf plot of this data to write a convincing argument about a reasonable length for a crocodile. Crocodile Average Lengths (ft) Source: Crocodilian Species List 22. FIND THE DATA Refer to the Data File on pages Choose some data that can be presented in a stem-and-leaf plot. Then analyze the stem-and-leaf plot to draw two conclusions about the data. H.O.T. Problems 23. FIND THE ERROR Rosita and Diana are Cut Ribbon Length analyzing the data in the stem-and-leaf Stem Leaf plot at the right. Diana says half of the pieces of ribbon are between 2 and 3 inches in length. Rosita says there are no pieces of ribbon more than 5 inches in length. Who is correct? Explain. 2 6 = 26 in. 24. CHALLENGE Create a stem-and-leaf plot in which the median of the data is 25. WRITING IN Present the data Fiber in Cereal (g) 25. MATH shown at the right in a line plot and a stem-and-leaf plot. Describe the similarities and differences among the representations. Which representation do you prefer to use? Explain your reasoning Lesson 8-3 Stem-and-Leaf Plots 413

23 26. COLLECT THE DATA Collect a set of data that represents the heights in inches of the people in your math class. Then write a question that can be solved by analyzing a stem-and-leaf plot of the data. Be sure to explain how the stem-and-leaf plot would be used to solve your problem. ISAT PRACTICE 1.A.3a, 1.A.3b 27. Denzell s science quiz scores are 11, 12, 13, 21, and 35. Which stem-and-leaf plot best represents this data? A Stem Leaf = 35 B Stem Leaf = 35 C Stem Leaf = 35 D Stem Leaf = The stem-and-leaf plot shows the points scored by the Harding Middle School basketball team. Points Scored Stem Leaf = 7 Which one of the following statements is true concerning how the measures of central tendency are affected by the inclusion of the outlier? F The mode is most affected. G The median is not affected. H The mean is most affected. J None of the measures of central tendency are affected. Find the mean, median, and mode for each set of data. Round to the nearest tenth if necessary. (Lesson 8-2) 29. 8, 23, 55, 58, 45, 32, 4, 55, , 2.4, 3., 7.9, 7.8, 2.4, 3.6, Make a line plot of the test scores shown. (Lesson 8-1) Test Scores 32. SCHOOL The ratio of boys to girls in the sixth grade is 7 to 8. How many girls are in the sixth grade if there are 56 boys? (Lesson 6-1) 33. Write _ 9 in simplest form. (Lesson 4-4) PREREQUISITE SKILL Choose an appropriate interval and scale for each set of data. (Lesson 8-1) 34. 9,, 18, 19, 2, 9, 8, 13, , 2, 6, 8, 9, 12, Chapter 8 Statistics: Analyzing Data

24 8-4 Bar Graphs and Histograms MAIN IDEA Display and analyze data using bar graphs and histograms. IL Learning Standards 1.A.3a Construct, read and interpret tables, graphs (including circle graphs) and charts to organize and represent data. New Vocabulary bar graph histogram FOOTBALL The table shows 5 teams that scored the greatest number of points in the Super Bowl. Team Score San Francisco 55 Dallas What is the greatest and least scores in the table? 2. How can you summarize the data with Tampa Bay Chicago Washington a visual representation? Source: National Football League 3. Do any of these representations show both the team and its score? A bar graph is a method of comparing data by using solid bars to represent quantities. IL Math Online glencoe.com Extra Examples Personal Tutor Self-Check Quiz Display Data Using a Bar Graph 1 Display the data in the table above in a bar graph. Step 1 Draw a horizontal axis and a vertical axis. Label the axes as shown. In this case, the scale on the vertical axis is 1 chosen so that it includes all the scores. Add a title. Score 5 Winning Super Bowl Teams San Francisco Dallas Tampa Bay Chicago Washington Teams Step 2 Draw a bar to represent each category. In this case, a bar is used to represent the score of each team. Score 5 Winning Super Bowl Teams San Francisco Dallas Tampa Bay Teams Chicago Washington Lesson 8-4 Bar Graphs and Histograms 415

25 a. FLOWERS The table shows the diameters of the world s largest flowers. Display the data in a bar graph. Flower Maximum Size (in.) Rafflesia 36 Sunflower 19 Giant Water Lily 18 Brazilian Dutchman 14 Magnolia 1 Source: Book of World Records Reading Math Frequency Frequency refers to the number of data items in a particular interval. In Example 2, the frequency of 7 in the third row means that there are 7 games with a score of A special kind of bar graph, called a histogram, uses bars to represent the frequency of numerical data that have been organized in intervals. Display Data Using a Histogram 2 FOOTBALL The winning scores of twenty recent Super Bowl games have been organized into a frequency table. Display the data in a histogram. Histograms Because the intervals are equal, all of the bars have the same width, with no space between them. Step 1 Step 2 Draw and label horizontal and vertical axes. Add a title. Draw a bar to represent the frequency of each interval. Score Frequency Source: National Football League Frequency Winning Super Bowl Scores Scores The three highest bars represent a majority of the data. From the graph, you can easily see that most of the scores were between 21 and 5 points. 416 Chapter 8 Statistics: Analyzing Data

26 b. EARTHQUAKES The magnitudes of Magnitude Frequency the largest U.S. earthquakes are organized into the frequency table shown. Display the data in a histogram Source: National Earthquake Information Center Alternate Method You can also use a proportion to find the percent in Example 4. 6_ 3 = x_ = 3 x 6 = 3 x 2 = x MALLS The histogram shows the number of stores in the largest malls in the U.S. 3 How many malls are represented in the histogram? Justify your answer. Find the sum of the heights of the bars in the histogram. So, = 3. 4 What percent of the malls had more than 274 stores? 6_ Interpret Histograms and Bar Graphs Frequency Largest U.S. Malls Source: Directory of Major Malls number of malls with more than 274 stores 3 total number of malls 6_ =.2 3 Write the fraction as a decimal..2 = 2% Write the decimal as a percent Number of Stores So, 2% of the malls had more than 274 stores. NASCAR The histogram shows the average winning times for the Daytona 5. c. How many winning times are represented in the histogram? Explain your reasoning. d. What percent of the winning speeds were faster than 15 miles per hour? Average Winning Speeds at Daytona 5 Frequency Winning Speeds (miles per hour) Lesson 8-4 Bar Graphs and Histograms 417

27 Examples 1, 2 (pp ) Select the appropriate graph to display each set of data: bar graph or histogram. Then display the data in the appropriate graph. 1. State Sales Tax Rates Percent States Source: Federation of Tax Administrators 2. Men s Grand Slam Titles Player Titles Pete Sampras 14 Roy Emerson 12 Bjorn Borg 11 Rod Laver 11 Andre Agassi 8 Source: Book of World Records Examples 3, 4 (p. 417) TEXTBOOKS For Exercises 3 and 4, use the bar graph that shows the average number of pages in various textbooks. 3. On average, which textbook has the least number of pages? 4. Is it reasonable to say that on average, a health textbook has half as many pages as a science textbook? Explain. Pages Health Textbook Size Math Science Textbook History HOMEWORK HELP For Exercises HELP See Examples 1, 2 3, 4 Select the appropriate graph to display each set of data: bar graph or histogram. Then display the data in the appropriate graph. 5. Most Threatened Reptiles Country Number of Species Australia 38 China 31 Indonesia 28 U.S. 27 India 25 Source: Top 1 of Everything 6. Home Run Leaders Home Runs Frequency Major U.S. Rivers Length (mi) Frequency , 1, ,4 1, ,8 2, ,2 2, City Skyscrapers City Skyscrapers New York 176 Hong Kong 163 Chicago 81 Shanghai 49 Tokyo 44 Source: The World Almanac Source: Book of World Records 418 Chapter 8 Statistics: Analyzing Data

28 HEIGHT For Exercises 9-12, use the histogram that shows the heights of students in a classroom. 9. How many students are from 5 to 59 inches tall? 1. What percent of students are at least 6 inches tall? 11. Write a statement comparing the 7 79 interval to the 6 69 interval. Frequency Students Heights Height (in.) 12. COLLECT THE DATA Conduct a survey of your classmates to determine their height. Then display and analyze the data in a histogram. How does your data compare to the histogram above? 7 79 Real-World Link Giraffes live for 1 15 years in the wild, but average 25 years at zoos. Source: Woodland Park Zoo ZOOS For Exercises 13 15, use the histogram that shows the attendance at the major U.S. zoos in a recent year. 13. About how many zoos does the graph represent? 14. What is the range of attendance for most of the zoos? 15. Compare the number of zoos with..9 million visitors to the number of zoos with million visitors. Frequency U.S. Zoo Attendance Source: The World Almanac Attendance (millions) Match each characteristic to the appropriate graph(s). 16. data display based upon place value a. line plot 17. shows the frequency of data on a number line b. histogram 18. compares data using solid bars c. stem-and-leaf plot 19. data are organized using intervals d. bar graph DISTANCE For Exercises 2 and 21, use the histogram shown below. Distance from School Frequency Distance (miles) How many students live 6 1 miles from school? 21. What percent of students live 16 or more miles from school? Daryl Balfour/Getty Images Lesson 8-4 Bar Graphs and Histograms 419

29 FOOD For Exercises 22 and 23, use the multiple-bar graph that compares boys and girls favorite pizza toppings 22. For which topping is the difference in girls and boys favorites the greatest? Explain. 23. Describe an advantage of using a multiple-bar graph rather than two separate graphs to compare data. Percent Favorite Pizza Toppings Girls Boys Pepperoni Sausage Cheese Ham Toppings EXERCISE For Exercises 24 27, refer to the graph below. 6 5 Favorite Sports to Play Girls Boys Percent Tennis Kickball Basketball Football Sports Volleyball Lacrosse Soccer ILS ISAT Extra Practice, pp. 688, Which sport did the girls surveyed prefer the most? 25. Which sport is the least favorite for the boys? 26. Based on this survey, boys prefer football 4 times more than what sport? 27. Is it reasonable to say that almost twice as many boys prefer basketball than girls? Explain. H.O.T. Problems 28. CHALLENGE The histograms show players salaries for two major league baseball teams. Compare the salary distributions of the two teams. Frequency Player Salaries: Team A Salary ($ million) Frequency Player Salaries: Team B Salary ($ million) DATA SENSE Describe how to determine the number of values in a data set that is represented by a histogram. WRITING IN 3. MATH Can any data set be displayed using a histogram? If yes, explain why. If no, give a counterexample and explain why not. 42 Chapter 8 Statistics: Analyzing Data

30 ISAT PRACTICE 31. The results of a survey are displayed in the graph. Number of Students Favorite Type of Book Romance Sci-Fi 1.A.3a Mystery Type of Book Adventure Which statement is valid about the survey? A Twice as many students enjoy reading mysteries than romance. B Most students enjoy reading adventure books. C Twice as many students enjoy reading romance books than science fiction. D Half as many students enjoy reading mysteries than romance. 32. SHORT RESPONSE The graph shows the average car sales per month at a car dealership. Number of Vehicles Sold Average Monthly Sales Sedan Station Wagon SUV Sport Coupe Type of Vehicle What is the best prediction for the number of station wagons the dealer sells in a year? SPORTS For Exercises 33 and 34, refer to the table that lists the number of games won by each team in a baseball league. 33. Make a stem-and-leaf plot of the data. (Lesson 8-3) 34. What is the mean, median, and mode of the data? (Lesson 8-2) 35. SELECT A TECHNIQUE The video game that Neil wants to buy costs $5. He has saved _ 1 of the amount he needs. Which of 5 the following techniques might Neil use to find how much more money he will need to buy the game? Justify your selection(s). Then use the technique(s) to solve the problem. (Lesson 5-5) mental math number sense estimation Number of Wins WEATHER At 5: p.m., the outside temperature was 81 F. At 6: p.m., it was 8 F. At 7: p.m., it was 79 F. Use the look for a pattern strategy to predict the outside temperature at 8: p.m. (Lesson 2-7) Lesson 8-4 Bar Graphs and Histograms 421

31 Extend 8-4 Spreadsheet Lab Circle Graphs MAIN IDEA Use technology to create circle graphs. IL Learning Standards 1.A.3a Construct, read and interpret tables, graphs (including circle graphs) and charts to organize and represent data. Another type of display used to compare categories of data is a circle graph. Circle graphs are useful when comparing parts of a whole. MAGAZINES The table shows the results of a survey in which students were asked to indicate their favorite type of magazine. Use a spreadsheet to make a circle graph of these data. Enter the data in a spreadsheet as shown. Magazine Preferences Type Frequency Comics 2 Fashion 7 Entertainment 5 News 3 Sports 6 Other 1 Magazine Preferences.xls A B C D E F Comics Fashion Entertainment News Sports Other Sheet 1 Sheet 2 Sheet 3 Magazine Preferences Comics Fashion Entertainment News Sports Other Select the information in cells A1 to B6. Click on the Chart Wizard icon. Choose the Pie chart type. Click Next twice. Enter the title Magazine Preferences. Then click Next and Finish. ANALYZE THE RESULTS 1. MAKE A CONJECTURE Use the graph to determine which types of magazines were preferred by about _ 1 and 25% of the students 3 surveyed. Explain your reasoning. Then check your answers. 2. COLLECT THE DATA Collect some data that can be displayed in either a circle or bar graph. Record the data in a spreadsheet. Then use the spreadsheet to make both types of displays. Which display is more appropriate? Justify your selection. 422 Chapter 8 Statistics: Analyzing Data

32 8 Mid-Chapter Quiz Lessons 8-1 through 8-4 IL Learning Standards 1.A.3a, 1.A.3b 1. MULTIPLE CHOICE The table shows quiz scores of a math class. What is the range of test scores? (Lesson 8-1) Math Scores A 89 C 67 B 82 D 28 For Exercises 2 4, use the data below. (Lesson 8-1) Age Upon Receiving Driver s License Make a line plot of the data. 3. Identify any clusters, gaps, or outliers. 4. Describe how the range of data would change if 25 was not part of the data set. 5. MULTIPLE CHOICE The table shows the average April rainfall for 12 cities. If the value 4.2 is added to this list, which of the following would be true? (Lesson 8-2) Average Rain (in.) F The mode would increase. G The mean would increase. H The mean would decrease. J The median would decrease. 6. TREES The heights, in meters, of several trees are 7.6, 6.8, 6.5, 7., 7.9, and 6.8. Find the mean, median, and mode. Round to the nearest tenth if necessary. (Lesson 8-2) 7. SPEED Display the Car Highway Speeds data shown in a stemand-leaf plot and write one conclusion based on the data. (Lesson 8-3) MAMMALS For Exercises 8 1, refer to the stem-and-leaf plot that shows the maximum weight in kilograms of several rabbits. Maximum Weight of Rabbits (kg) Stem Leaf =.8 kg 8. Find the range of weights. 9. Find the median and mode of the data. 1. Which measure of central tendency is most affected by the inclusion of the outlier? Explain. ATTENDANCE For Exercises 11 and 12, refer to the graph. (Lesson 8-4) Attendance College Football Stadiums 12, 1, 8, 6, Source: MSNBC Kyle Field Memorial Neyland Notre Dame Tiger Stadium College Stadium 11. About how many people does the graph represent? 12. Which two stadiums house about the same number of people? Chapter 8 Mid-Chapter Quiz 423