Lesson 1 Contents Example 1Make a Frequency Table Example 2Make and Use a Frequency Table Example 3Interpret Data
Example 1-1a FOOTBALL Winning Super Bowl scores from 1983 to 2002 are listed below. Make a frequency table of the data. interval: 9 scale: 20 to 55 The scale includes all of the data, and the interval separates it into equal parts. Step 1 Choose an appropriate interval and scale for the data. The scale should include the least value, 20, and the greatest value, Winning Scores Source: superbowl.com
FrequencyTallyScores Example 1-1a Step 2 Draw a table with three columns and label the columns Scores, Tally, and Frequency. Step 3 Complete the table. Answer: IIII I 3III IIII IIII I20-28
Example 1-1b 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. Answer: High Temperature ( F) II IIII II IIII I60-69 FrequencyTallyPoints
FPPRJ FRRJC PCFPF PPFRF FPFRP Favorite Types of Music R=rock, J=jazz, C=country, F=top 40, P=rap Example 1-2a 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.
8IIII III 8 2II 2 5IIII FrequencyTally Draw a table with three columns. Example 1-2a Answer: The two favorite types were top 40 and rap, with 8 tallies. The least favorite types were jazz, and country, with 2 tallies. rap top 40 country jazz rock Music In the first column, list the types of music. Then complete the rest of the table.
Example 1-2b 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. YBYPY RYBPR YLRYP LPBRY Favorite Colors Y=yellow, R=red, B=blue, P=pink, L=purple
Example 1-2b Answer: The favorite color is yellow with 7 tallies, and purple is the least favorite color with 2 tallies. 2IIpurple 4IIIIpink 3IIIblue 4IIIIred 7IIII IIyellow FrequencyTallyColor
Example 1-3a 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 1I130–135 2II124–129 14IIII IIII IIII118–123 16IIII IIII IIII I112–117 IIII IIII II106–111 IIII100–105 Tally Temp ( F)
Example 1-3a There are four categories with temperatures above 111 . Answer: So, of the states reported temperatures above 111 . states state
Example 1-3b 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? Answer: Frequency 1I IIII IIII III IIII II90-99 IIII80-89 III70-79 TallyWeight
End of Lesson 1
Lesson 2 Contents Example 1Use a Line Graph to Predict Example 2 Use a Scatter Plot to Predict
Example 2-1a 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
Example 2-1a Answer: It will take Enrique about 14 minutes to type his 600-word paper.
Example 2-1b 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
Example 2-1b Answer: In 12 hours, Helen will travel about 700 miles.
Example 2-2a 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 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 2-2b 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
End of Lesson 2
Lesson 3 Contents Example 1Make a Line Plot Example 2Use a Line Plot to Analyze Data Example 3Use a Line Plot to Analyze Data
Example 3-1a 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 Age at Inauguration Source: Factmonster.com
Example 3-1a 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 3-1b 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 3-2a 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 3-2b 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 3-3b 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 3-2b 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.
End of Lesson 3
Lesson 4 Contents Example 1Find the Mean Example 2Find the Mean, Median, and Mode Example 3Analyze Data
Example 4-1a 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 Number of Species in Major U.S. Zoos
Example 4-1a sum of data number of data items Answer: The mean number of species of animals is
Example 4-1b 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. Answer: hours Nightly Hours of Sleep
Example 4-2a 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 Winter Olympics: Gold Medals Won
Example 4-2a 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 4-2b 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. Answer: mean: 1.44; median: 1; mode: Pets
Example 4-3a 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 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 4-3b 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.
End of Lesson 4
Lesson 5 Contents Example 1Construct a Stem-and-Leaf Plot Example 2Analyze Data Example 3Make Conclusions About Data
Example 5-1a 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 Home Runs
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 3Order the leaves and write a key that explains how to read the stems and leaves. Example 5-1a 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.
Example 5-1a Answer: LeafStem 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 5-1b 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 Answer: LeafStem 1|3 = 13 hours
Example 5-2a 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 LeafStem 2|5 = 25 miles
Example 5-2a median:middle value, or 12 miles mode:most frequent value, or 10 miles range:greatest distance – least distance 30 – 5 or 25 miles Answer: range: 25 miles; median: 12 miles; mode: 10 miles
Example 5-2b 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. Answer: range: 25 inches; median: 10 inches; mode: 10 inches Leaf Stem 1|2 = 12 inches
Example 5-3a 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 15Zebra10Giraffe20Chimpanzee 16Tiger40Elephant12Cat 10Squirrel12Dog12Camel 3Mouse8Deer20Polar Bear 20Horse15Cow18Black Bear 4Guinea Pig6Chipmunk20Baboon YearsAnimalYearsAnimalYearsAnimal
Example 5-3a 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: LeafStem 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 5-2b 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 Most students scored above 75. The mode is is an outlier with a significant gap between that value and the next highest value. Answer: LeafStem 7|5 = 75 points
End of Lesson 5
Lesson 6 Contents Example 1Construct a Box-and-Whisker Plot Example 2Analyze Data Example 3Identify and Plot Outliers
Example 6-1a 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. 7Tuna18Ground beef 9Trout10Fried shrimp 9Sardines 3Fish sticks 5Salmon 3Crabmeat 5Roast beef16Bologna 19Pork chop15Beefsteak 14Ham 9Bacon Fat (gm)ItemFat (gm)Item Nutrition Facts Source: The World Almanac
3, 3, 5, 5, 7, 9, 9, 9, 10, 14, 15, 16, 18, 19 Example 6-1a Step 2 Find the median and the quartiles. Step 1 Order the data from least to greatest. median: 9 lower quartile: median of lower half = 5 upper quartile: median of upper half = 15
Example 6-1a 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. Answer:
Example 6-1b 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 6-2a 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 PlayerGoalsPlayerGoals Wayne Gretzky894Steve Yzerman645 Gordie Howe801Phil Esposito717 Marcel Dionne731Ray Bourque410 Mark Messler627Mario Lemieux648 Ron Francis487Paul Coffey396 Source: The World Almanac
Example 6-2a Find the median, the quartiles, and the extremes. Then construct the plot.
Example 6-2a 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 6-2b 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 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 6-3a 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. Find the median and the quartiles Candy Sold per Student
Example 6-3a Next, determine whether there are any outliers. So, outliers are data more than 1.5(15) or 22.5 from the quartiles. 20 and 80 are limits for the outliers.
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. Example 6-3a Answer:
Example 6-3b 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:
End of Lesson 6
Lesson 7 Contents Example 1Construct a Bar Graph Example 2Construct a Histogram Example 3Compare Bar Graphs and Histograms Example 4Use Graphs to Solve a Problem
Example 7-1a 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. 13United States 25Japan 25Korea 26Canada 28United Kingdom 34Brazil 35Germany 37France 42Italy Vacation Days per YearCountry Source: The World Almanac
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
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. Example 7-1a Answer:
Example 7-1b 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 Tamika12 David14 Anne 8 Jonas 5 Hana10
Example 7-1b Answer:
Example 7-2a 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
Example 7-2a 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 7-2b 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 – – – – 89 3
Example 7-2b Answer:
Example 7-3a AUTOMOBILES Refer to the graphs below.
Example 7-3a Answer: Graph A Which graph would you use to tell how many cars under $30,000 were sold? Which graph would you use to compare the prices of a mid-size car and an SUV? Answer: Graph B
Example 7-3b HOUSING Refer to the graphs below.
Example 7-3b 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 7-4a 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 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. Read the Test Item Determine which of the four statements is not correct. Solve the Test Item 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 7-4b Answer: B 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
End of Lesson 7
Lesson 8 Contents Example 1Misleading Graphs Example 2Misleading Statistics
Example 8-1a 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 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 8-1b 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 8-2a 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. Test Grade (%) MichaelMelissa MichaelMelissa mean 53.4% 71.9% median 70% 70% 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 8-2b 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. ItemStore 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 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.
End of Lesson 8
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