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Mathematics: Application and Concepts, Course 2 Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc., Cincinnati, Ohio Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio Welcome to Interactive Chalkboard

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**Lesson 2-1 Frequency Tables Lesson 2-2 Making Predictions **

Lesson 2-3 Line Plots Lesson 2-4 Mean, Median, and Mode Lesson 2-5 Stem-and-Leaf Plots Lesson 2-6 Box-and-Whisker Plots Lesson 2-7 Bar Graphs and Histograms Lesson 2-8 Misleading Statistics Contents

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**Example 1 Make a Frequency Table **

Example 2 Make and Use a Frequency Table Example 3 Interpret Data Lesson 1 Contents

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**FOOTBALL Winning Super Bowl scores from 1983 to 2002 are listed below**

FOOTBALL Winning Super Bowl scores from 1983 to 2002 are listed below. Make a frequency table of the data. 27 38 46 39 42 20 55 37 52 30 49 35 31 34 23 Winning Scores Source: superbowl.com Step 1 Choose an appropriate interval and scale for the data. The scale should include the least value, 20, and the greatest value, 55. interval: 9 scale: 20 to 55 The scale includes all of the data, and the interval separates it into equal parts. Example 1-1a

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**Step 3 Complete the table.**

Step 2 Draw a table with three columns and label the columns Scores, Tally, and Frequency. Step 3 Complete the table. Answer: Frequency Tally Scores IIII I 3 III 47-55 5 IIII 38-46 6 29-37 20-28 Example 1-1a

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TEMPERATURE The daily high temperatures for the last two weeks of August in Cleveland, Ohio are listed below. Make a frequency table of the data. High Temperature (F) Answer: 2 II 90-99 7 IIII II 80-89 4 IIII 70-79 1 I 60-69 Frequency Tally Points Example 1-1b

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**Favorite Types of Music**

MUSIC Kaley asked her classmates about their favorite types of music. The results are shown in the table. Make a frequency table of the data. Then determine the favorite and least favorite types of music. F P R J C Favorite Types of Music R=rock, J=jazz, C=country, F=top 40, P=rap Example 1-2a

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**Draw a table with three columns. **

In the first column, list the types of music. Then complete the rest of the table. rap top 40 country jazz rock Music 8 IIII III 2 II 5 IIII Frequency Tally Answer: The two favorite types were top 40 and rap, with 8 tallies. The least favorite types were jazz, and country, with 2 tallies. Example 1-2a

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**COLORS Samantha asked her classmates about their favorite colors**

COLORS Samantha asked her classmates about their favorite colors. The results are shown in the table. Make a frequency table of the data. Then determine the favorite and least favorite colors. Y B P R L Favorite Colors Y=yellow, R=red, B=blue, P=pink, L=purple Example 1-2b

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Answer: The favorite color is yellow with 7 tallies, and purple is the least favorite color with 2 tallies. 2 II purple 4 IIII pink 3 III blue red 7 IIII II yellow Frequency Tally Color Example 1-2b

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TEMPERATURE The frequency table shows the record high temperatures reported by each state of the United States. How many states have reported temperatures above 111? 12 5 Frequency 1 I 130–135 2 II 124–129 14 IIII IIII IIII 118–123 16 IIII IIII IIII I 112–117 IIII IIII II 106–111 IIII 100–105 Tally Temp (F) Example 1-3a

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**There are four categories with temperatures above 111.**

states states states state Answer: So, of the states reported temperatures above 111. Example 1-3a

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WEIGHT The frequency table shows the results of a survey of the weights of boys in a seventh grade class. How many of the boys weigh less than 100 pounds? 5 3 Frequency 1 I 4 IIII 8 IIII III 7 IIII II 90-99 80-89 III 70-79 Tally Weight Answer: 15 Example 1-3b

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End of Lesson 1

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**Example 1 Use a Line Graph to Predict **

Example 2 Use a Scatter Plot to Predict Lesson 2 Contents

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**TYPING Enrique is writing a 600-word paper for class**

TYPING Enrique is writing a 600-word paper for class. The table shows the time it has taken Enrique to type the paper so far. Make a line graph and predict the total time it will take him to type his paper. Time (min) Words Typed 1 40 2 85 3 128 4 169 5 214 6 258 Example 2-1a

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**It will take Enrique about 14 minutes to type his 600-word paper.**

Answer: It will take Enrique about 14 minutes to type his 600-word paper. Example 2-1a

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**Total Travel Time (hours)**

TRAVEL During a recent road trip, Helen kept track of the number of miles traveled after each hour of travel time was completed. The table below shows her information. Make a line graph and predict how far Helen will travel in 12 hours of travel time. Total Travel Time (hours) Miles 1 52 2 110 3 171 4 225 5 290 6 348 Example 2-1b

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**In 12 hours, Helen will travel about 700 miles.**

Answer: In 12 hours, Helen will travel about 700 miles. Example 2-1b

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POLLUTION The scatter plot shows the number of days that San Bernardino, California, failed to meet air quality standards from 1990 to Use it to predict the number of days of bad air quality in 2004. Example 2-2a

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Answer: By looking at the pattern in the graph, we can predict that the number of days of bad air quality in 2004 will be about 48 days. Example 2-2a

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GAS MILEAGE The scatter plot shows the gas mileage based on the weight of a car. Use it to predict the gas mileage for a car weighing 5500 pounds. Answer: 20 mpg Example 2-2b

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End of Lesson 2

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**Example 1 Make a Line Plot Example 2 Use a Line Plot to Analyze Data **

Lesson 3 Contents

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**PRESIDENTS The table below shows the ages of the U. S**

PRESIDENTS The table below shows the ages of the U.S. presidents at the time of their inaugurations. Make a line plot of the data. 56 55 51 46 43 42 54 68 62 52 61 60 65 57 48 58 64 47 50 69 49 Age at Inauguration Source: Factmonster.com Example 3-1a

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Step 1 Draw a number line. The youngest president was 42 and the oldest was 69, so you can use a scale of 40 to 70 and an interval of 5. Step 2 Place an above the number that represents the age of each U.S. president at the time of their inauguration. Answer: Example 3-1a

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STUDY TIME The table below shows the number of minutes each student in a math class spent studying the night before the last math exam. Make a line plot of the data. Minutes Studying Answer: Example 3-1b

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CLIMATE The line plot shows the number of inches of precipitation that fell in several cities west of the Mississippi River during a recent year. What is the range of the data? The greatest amount of precipitation is 50 inches, and the lowest amount of precipitation is 5 inches. Answer: The range of the amounts of precipitation is 50–5 or 45 inches. Example 3-2a

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AGE The line plot below shows the ages of students in an introductory computer course at the local community college. What is the range of the data? Answer: 26 years Example 3-2b

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Identify clusters, gaps, and outliers if any exist in the line plot below and explain what they mean. Answer: There are data clusters between 11 and 13 inches and between 16 and 18 inches. At least half of the data fall below 25, so most of the selected cities west of the Mississippi River had fewer than 25 inches of precipitation. Example 3-3b

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Identify clusters, gaps, and outliers if any exist in the line plot below and explain what they mean. Answer: There is a gap between 30 years and 44 years. The age 44 appears to be removed from the rest of the data, so it could be considered an outlier. This means that 44 years old is a high age relative to the rest of the class and is not representative of the whole class. Example 3-2b

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End of Lesson 3

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**Example 2 Find the Mean, Median, and Mode Example 3 Analyze Data**

Lesson 4 Contents

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ANIMALS The table below shows the number of species of animals found at 30 major zoos across the United States. Find the mean. Source: The World Almanac 659 300 800 400 705 350 232 640 435 488 347 195 133 290 280 715 700 617 175 283 Number of Species in Major U.S. Zoos Example 4-1a

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**Answer: The mean number of species of animals is**

sum of data number of data items Answer: The mean number of species of animals is Example 4-1a

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SLEEP The table below shows the results of a survey of 15 middle school students concerning the number of hours of sleep they typically get each night. Find the mean. Nightly Hours of Sleep Answer: hours Example 4-1b

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OLYMPICS The table below shows the number of gold medals won by each country participating in the 2002 Winter Olympic games. Find the mean, median, and mode of the data. Source: CBSSportsline.com 1 2 4 3 11 6 10 12 2002 Winter Olympics: Gold Medals Won Example 4-2a

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**mean: sum of data divided by 25, or 3.16**

median: 13th number of the ordered data, or 2 mode: number appearing most often, or 0 Answer: mean: 3.06; median: 2; mode: 0 Example 4-2a

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**Answer: mean: 1.44; median: 1; mode: 0**

PETS The table below shows the number of pets students in an art class at Green Hills Middle School have at home. Find the mean, median, and mode of the data. Pets Answer: mean: 1.44; median: 1; mode: 0 Example 4-2b

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FIRST FAMILIES The line plot in the bottom margin shows the number of children of United States presidents. Would the mean, median, or mode best represent the number of children? Example 4-3a

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**Answer: The mean, median, and mode are close with. values of 3. 1, 2**

Answer: The mean, median, and mode are close with values of 3.1, 2.5, and 2 respectively. Any of the three could be used to represent the data. Example 4-3a

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SIBLINGS The line plot below shows the number of siblings of each student in a particular classroom. Would the mean, median, or mode best represent the number of siblings? Answer: The mean, median, and mode are close with values of 1.84, 2, and 2 respectively. Any of the three could be used to represent the data. Example 4-3b

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End of Lesson 4

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**Example 1 Construct a Stem-and-Leaf Plot Example 2 Analyze Data **

Example 3 Make Conclusions About Data Lesson 5 Contents

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BASEBALL The table below shows the number of home runs that Babe Ruth hit during his career from 1914 to Make a stem-and-leaf plot of the data. Source: baberuth.com 49 46 29 22 11 6 54 41 2 34 60 35 3 47 59 4 25 Home Runs Example 5-1a

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Step 1 The digits in the least place value will form the leaves and the remaining digits will form the stems. In this data, 0 is the least value, and 60 is the greatest. So, the ones digit will form the leaves and the tens digit will form the stems. Step 2 List the stems 0 to 6 in order from least to greatest in the Stem column. Write the leaves, the ones digits of the home runs, 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. Example 5-1a

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Answer: 6 5 4 4 5 3 2 1 Leaf Stem 2|5 = 25 home runs A key shows how the digits are related. The ones digits of the data form the leaves. The tens digits of the data form the stems. Example 5-1a

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**Hours Aboard an Airplane**

BUSINESS The table below shows the number of hours spent aboard an airplane for a survey of business men and women. Make a stem-and-leaf plot of the data. Hours Aboard an Airplane Example 5-1b

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Answer: 5 3 2 1 Leaf Stem 1|3 = 13 hours Example 5-1b

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FITNESS The stem-and-leaf plot below shows the number of miles that Megan biked each day during July. Find the range, median, and mode of the data. 3 2 1 Leaf Stem 2|5 = 25 miles Example 5-2a

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**range: greatest distance – least distance 30 – 5 or 25 miles**

median: middle value, or 12 miles mode: most frequent value, or 10 miles Answer: range: 25 miles; median: 12 miles; mode: 10 miles Example 5-2a

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**Answer: range: 25 inches; median: 10 inches; mode: 10 inches**

SNOWFALL The stem-and-leaf plot below shows the number of inches of snow that fell in Hightown during the month of January for the past 15 years. Find the range, median, and mode. 2 6 Leaf 2 1 Stem 1|2 = 12 inches Answer: range: 25 inches; median: 10 inches; mode: 10 inches Example 5-2b

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**ANIMALS The table shows the average life span of several animals**

ANIMALS The table shows the average life span of several animals. Make a stem-and-leaf plot of the data. Then use it to describe how the data are spread out. Source: The World Almanac 15 Zebra 10 Giraffe 20 Chimpanzee 16 Tiger 40 Elephant 12 Cat Squirrel Dog Camel 3 Mouse 8 Deer Polar Bear Horse Cow 18 Black Bear 4 Guinea Pig 6 Chipmunk Baboon Years Animal Example 5-3a

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**The least value is 3, and the greatest value is 40**

The least value is 3, and the greatest value is 40. So, the tens digits form the stems, and the ones digits form the leaves. Answer: 4 3 2 1 Leaf Stem 1|0 = 10 years Most animals live less than 20 years. The mode is is an outlier with a significant gap between that value and the next smaller value. Example 5-3a

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TEST SCORES The table below shows the test scores earned by a class of middle school math students on a chapter test. Make a stem-and-leaf plot of the data. Then use it to describe how the data are spread out. Test Scores Example 5-2b

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**Most students scored above 75. The mode is 93**

Most students scored above 75. The mode is is an outlier with a significant gap between that value and the next highest value. Answer: 9 8 7 6 5 Leaf Stem 7|5 = 75 points Example 5-2b

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End of Lesson 5

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**Example 1 Construct a Box-and-Whisker Plot Example 2 Analyze Data **

Example 3 Identify and Plot Outliers Lesson 6 Contents

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NUTRITION The grams of fat per serving of items from the meat, poultry, and fish food group are shown in the table. Make a box-and-whisker plot of the data. 7 Tuna 18 Ground beef 9 Trout 10 Fried shrimp Sardines 3 Fish sticks 5 Salmon Crabmeat Roast beef 16 Bologna 19 Pork chop 15 Beefsteak 14 Ham Bacon Fat (gm) Item Nutrition Facts Source: The World Almanac Example 6-1a

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**Step 1 Order the data from least to greatest.**

Step 2 Find the median and the quartiles. median: 9 3, 3, 5, 5, 7, 9, 9, 9, 10, 14, 15, 16, 18, 19 lower quartile: median of lower half = 5 upper quartile: median of upper half = 15 Example 6-1a

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**Step 4 Draw the box and whiskers.**

Step 3 Draw a number line. The scale should include the median, the quartiles, and the lower and upper extremes. Graph the values as points above the line. Step 4 Draw the box and whiskers. Answer: Example 6-1a

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ATTENDANCE The number of students attending class each day are shown in the table. Make a box-and-whisker plot of the data. Attendance Answer: Example 6-1b

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HOCKEY The table shows the ten all-time leading scorers in the National Hockey League through a recent season. Make a box-and-whisker plot of the data. Then use it to describe how the data are spread. NHL Leading Scorers Player Goals Wayne Gretzky 894 Steve Yzerman 645 Gordie Howe 801 Phil Esposito 717 Marcel Dionne 731 Ray Bourque 410 Mark Messler 627 Mario Lemieux 648 Ron Francis 487 Paul Coffey 396 Source: The World Almanac Example 6-2a

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**Find the median, the quartiles, and the extremes**

Find the median, the quartiles, and the extremes. Then construct the plot. Example 6-2a

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Answer: The graph shows that half of the players scored between 487 and 731 points. The largest range of the four quartiles is from 731 to 894. One-fourth of the players scored within this range. Example 6-2a

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COMMUTE The table below shows the commute time from home to school for fifteen middle school students. Make a box-and-whisker plot of the data. Then use it to describe how the data are spread. Commute Time Example 6-2b

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Answer: The graph shows that half of the students travel between 10 and 21 minutes. The largest range of the four quartiles is from 21 to 46. One-fourth of the commute times are within this range. Example 6-2b

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**Find the median and the quartiles.**

CANDY SALES Twelve members of the music club sold candy bars as a fund-raiser. The table shows the number of candy bars sold by each person. Make a box-and-whisker plot of the data. 55 39 54 46 53 81 51 60 27 69 23 Candy Sold per Student Find the median and the quartiles. Example 6-3a

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**Next, determine whether there are any outliers.**

So, outliers are data more than 1.5(15) or from the quartiles. 20 and 80 are limits for the outliers. Example 6-3a

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**Any data point that is less than 20 or greater than 80 is an outlier**

Any data point that is less than 20 or greater than 80 is an outlier. So, 81 is an outlier. Plot the outlier using a dot. Answer: Example 6-3a

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BASKETBALL The table below shows the number of points scored by the leading scorer of a basketball team during the past twelve games. Make a box-and-whisker plot of the data. Points Scored Answer: Example 6-3b

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End of Lesson 6

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**Example 1 Construct a Bar Graph Example 2 Construct a Histogram **

Example 3 Compare Bar Graphs and Histograms Example 4 Use Graphs to Solve a Problem Lesson 7 Contents

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TOURISM The table below shows the average number of vacation days per year for people in various countries. Make a bar graph to display the data. 13 United States 25 Japan Korea 26 Canada 28 United Kingdom 34 Brazil 35 Germany 37 France 42 Italy Vacation Days per Year Country Source: The World Almanac Example 7-1a

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**Step 1 Draw a horizontal axis and a vertical axis**

Step 1 Draw a horizontal axis and a vertical axis. Label the horizontal axis with the countries and the vertical axis with the number of vacation days. The scale on vertical axis is chosen so that it includes all of the vacation days per year. Example 7-1a

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**Step 2 Draw a bar to represent each category**

Step 2 Draw a bar to represent each category. In this case, a bar is used to represent the number of vacation days per year for each country. Answer: Example 7-1a

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SPORTS The table below shows the average number of miles run each day during training by members of the cross country track team. Make a bar graph to display the data. Runner Miles Run Each Day Bob 9 Tamika 12 David 14 Anne 8 Jonas 5 Hana 10 Example 7-1b

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Answer: Example 7-1b

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**Number of Wins Frequency**

BASKETBALL The number of wins for the 29 teams of the NBA for the season have been organized into a frequency table. Make a histogram of the data. Number of Wins Frequency 11-20 3 21-30 4 31-40 41-50 10 51-60 8 Example 7-2a

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**Step 1 Draw and label horizontal and vertical axes. Add a title.**

Step 2 Draw a bar to represent the frequency of each interval. Answer: Example 7-2a

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SPEED The speeds of cars on a stretch of interstate are clocked by a police officer and have been organized into a frequency table. Make a histogram of the data. Speed (mph) Frequency 50 – 59 2 60 – 69 14 70 – 79 18 80 – 89 3 Example 7-2b

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Answer: Example 7-2b

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**AUTOMOBILES Refer to the graphs below.**

Example 7-3a

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**Which graph would you use to tell how many cars under $30,000 were sold?**

Answer: Graph A Which graph would you use to compare the prices of a mid-size car and an SUV? Answer: Graph B Example 7-3a

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**HOUSING Refer to the graphs below.**

Example 7-3b

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**Which graph would you use to tell how many houses sold for $150,000 or greater in a recent year?**

Which graph would you use to compare the price of a ranch style home to the price of a colonial style home? Answer: Graph B Answer: Graph A Example 7-3b

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**A There are 67 cars in the data set.**

MULTIPLE- CHOICE TEST ITEM Which conclusion cannot be made about the data in the graph? A There are 67 cars in the data set. B Two cars are priced between $30,000 and $34,999. C Most of the cars are priced between $15,000 and $19,999. D Mid-size cars sell the best. Example 7-4a

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**B is correct; the bar representing $30,000-$34,999 has a value of 2.**

Read the Test Item Determine which of the four statements is not correct. Solve the Test Item A is correct; 30 cars are priced between $15,000 and $19,999, 25 cars are priced between $20,000 and $24,999, and so on, for a total of 67 cars. B is correct; the bar representing $30,000-$34,999 has a value of 2. C is correct; the bar representing $15,000-$19,999 is the highest. D is incorrect; the graph does not distinguish among different car types. Answer: D Example 7-4a

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**A There are 21 homes in the $150,000 - $199,000 interval. **

MULTIPLE- CHOICE TEST ITEM Which conclusion cannot be made about the data in the graph? A There are 21 homes in the $150,000 - $199,000 interval. B Colonial style homes tend to cost more than ranch style homes. C A total of 79 homes are in the data set. D The most houses are priced between $200,000 and $249,000 Answer: B Example 7-4b

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End of Lesson 7

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**Example 1 Misleading Graphs Example 2 Misleading Statistics**

Lesson 8 Contents

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BUSINESS The line graphs below show the last 10 weeks of sales for the Crumby Cookie Bakery. Which graph would be better to help convince a bank loan officer to open a $20,000 loan to remodel a kitchen? Why might this graph be considered misleading? Example 8-1a

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Answer: Graph A would be better because it shows less of a decline in sales. It might be considered misleading because it does not show the consistent decline in sales. Example 8-1a

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Profit The line graph below shows the monthly profits of a company from May to October. Explain why the graph is misleading. Answer: The graph is misleading because the vertical scale has differing intervals. The increases in profits are exaggerated. Example 8-1b

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GRADES Michael and Melissa both claim to be earning a C average, 70% to 79%, in their Latin class. Use the table below to explain their reasoning and determine which student is earning a C average. Michael Melissa mean % % median 70% 70% Test Grade (%) Michael Melissa 1 80 88 2 76 83 3 73 75 4 70 5 40 60 6 25 65 7 10 62 Answer: Michael is using the median to describe his grade rather than the mean. Only Melissa’s mean or average is 70% or better. Example 8-2a

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RETAIL SALES Two different grocery stores each claim to have the lowest average prices. Use the table below to explain their reasoning and determine which store really has the lowest average prices. Answer: Store A: mean $3.19, median $2.14, Store B: mean $2.79, median $2.42. Store A is using the median to describe its average prices rather than the mean. Store B has the lowest average price. Item Store A Price Store B Price Milk $1.29 $1.34 Bread $1.99 $1.85 Eggs $1.19 $1.09 Soda $2.29 $2.99 Coffee $7.99 $5.29 Ice Cream $4.39 $4.19 Example 8-2b

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End of Lesson 8

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**Explore online information about the information introduced in this chapter.**

Click on the Connect button to launch your browser and go to the Mathematics: Applications and Concepts, Course 2 Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to Online

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