Data Analysis and Displays

Transcription

1 9 Data Analsis and Displas 9. Scatter Plots 9. Lines of Fit 9.3 Two-Wa Tables 9.4 Choosing a Data Displa Wow. The number of minutes I can dog paddle is growing like craz! The price of dog biscuits is up again this month. But I have a reall good feeling about November.

2 What You Learned Before Eample Plot (a) ( 3, ) and (b) (4,.5) in a coordinate plane. Describe the location of each point. ( 3, ) O (4,.5) Here s an interesting surve about favorite dog tos. a. Start at the origin. Move 3 units left and units up. Then plot the point. The point is in Quadrant II. b. Start at the origin. Move 4 units right and.5 units down. Then plot the point. The point is in Quadrant IV. Plot the ordered pair in a coordinate plane. Describe the location of the point.. (, 3). (, 4) 3. (, 3.5) 4. ( 3 4, 4) Eample Write in slope-intercept form an equation of the line that passes through the points (4, ) and (, 8). Find the slope: m = = 8 4 = 5 = Then use the slope m = and the point (4, ) to write an equation of the line. = m( ) Write the point-slope form. = ( 4) Substitute for m, 4 for, and for. = 8 = 6 Distributive Propert Write in slope-intercept form. Write in slope-intercept form an equation of the line that passes through the given points. 5. (, 4), (3, 8) 6. (, ), ( 8, ) 7. (6, 8), (3, 9)

3 9. Scatter Plots How can ou construct and interpret a scatter plot? ACTIVITY: Constructing a Scatter Plot Work with a partner. The weights (in ounces) and circumferences C (in inches) of several sports balls are shown. Basketball Soccer Baseball Tennis 5 oz 9 in. oz 3 in. Golf oz 8 in..6 oz 5.3 in. 6 oz 8 in. Water Polo Softball Racquetball.4 oz 7 in. 7 oz in. 5 oz 7 in. Data Analsis In this lesson, ou will construct and interpret scatter plots. describe patterns in scatter plots. Learning Standard 8.SP. b. Write the weight and circumference C of each ball as an ordered pair. Then plot the ordered pairs in the coordinate plane. c. Describe the relationship between weight and circumference. Are an of the points close together? d. In general, do ou think ou can describe this relationship as positive or negative? linear or nonlinear? Eplain. oz 6 in. C Circumference (inches) a. Choose a scale for the horizontal ais and the vertical ais of the coordinate plane shown. COMMON CORE Volleball V Weight (ounces) e. A bowling ball has a weight of 5 ounces and a circumference of 7 inches. Describe the location of the ordered pair that represents this data point in the coordinate plane. How does this point compare to the others? Eplain our reasoning. 37 Chapter 9 Data Analsis and Displas

4 ACTIVITY: Constructing a Scatter Plot Math Practice Recognize Usefulness of Tools How do ou know when a scatter plot is a useful tool for making a prediction? Work with a partner. The table shows the number of absences and the final grade for each student in a sample. a. Write the ordered pairs from the table. Then plot them in a coordinate plane. b. Describe the relationship between absences and final grade. How is this relationship similar to the relationship between weight and circumference in Activit? How is it different? c. MODELING A student has been absent 6 das. Use the data to predict the student s final grade. Eplain how ou found our answer. Absences Final Grade ACTIVITY: Identifing Scatter Plots Work with a partner. Match the data sets with the most appropriate scatter plot. Eplain our reasoning. a. month of birth and birth weight for infants at a da care b. quiz score and test score of each student in a class c. age and value of laptop computers i. ii. iii. 4. How would ou define the term scatter plot? 5. IN YOUR OWN WORDS How can ou construct and interpret a scatter plot? Use what ou learned about scatter plots to complete Eercise 7 on page 376. Section 9. Scatter Plots 373

5 9. Lesson Lesson Tutorials Ke Vocabular scatter plot, p. 374 Scatter Plot A scatter plot is a graph that shows the relationship between two data sets. The two sets of data are graphed as ordered pairs in a coordinate plane. EXAMPLE Interpreting a Scatter Plot Calories Restaurant Sandwiches Fat (grams) The scatter plot at the left shows the amounts of fat (in grams) and the numbers of calories in restaurant sandwiches. a. How man calories are in the sandwich that contains 7 grams of fat? Restaurant Sandwiches Draw a horizontal line from the point that has 8 an -value of 7. It 75 crosses the -ais at 4. So, the sandwich has 4 calories. b. How man grams of fat are in the sandwich that contains 6 calories? Draw a vertical line from the point that has a -value of 6. It crosses the -ais at 3. Calories Fat (grams) So, the sandwich has 3 grams of fat. c. What tends to happen to the number of calories as the number of grams of fat increases? Looking at the graph, the plotted points go up from left to right. So, as the number of grams of fat increases, the number of calories increases. Eercises 8 and 9. WHAT IF? A sandwich has 65 calories. Based on the scatter plot in Eample, how man grams of fat would ou epect the sandwich to have? Eplain our reasoning. 374 Chapter 9 Data Analsis and Displas

6 A scatter plot can show that a relationship eists between two data sets. Positive Linear Negative Linear Nonlinear Relationship Relationship Relationship No Relationship O O O O The points lie close to a line. As increases, increases. The points lie close to a line. As increases, decreases. The points lie in the shape of a curve. The points show no pattern. EXAMPLE Identifing Relationships Describe the relationship between the data. Identif an outliers, gaps, or clusters. a. television size and price b. age and number of pets owned Television Size and Price Age and Pets Owned Price (dollars) Number of pets owned Television size (inches) Person s age (ears) The points appear to lie close to a line. As increases, increases. So, the scatter plot shows a positive linear relationship. There is an outlier at (7, 5), a cluster of data under $5, and a gap in the data from $5 to $5. The points show no pattern. So, the scatter plot shows no relationship. There are no obvious outliers, gaps, or clusters in the data. Eercises. Make a scatter plot of the data and describe the relationship between the data. Identif an outliers, gaps, or clusters. Stud Time (min), Test Score, Section 9. Scatter Plots 375

7 9. Eercises Help with Homework. VOCABULARY What tpe of data do ou need to make a scatter plot? Eplain.. REASONING How can ou identif an outlier in a scatter plot? LOGIC Describe the relationship ou would epect between the data. Eplain. 3. shoe size of a student and the student s IQ 4. time since a train s departure and the distance to its destination 5. height of a bouncing ball and the time since it was dropped 6. number of toppings on a pizza and the price of the pizza 9+(-6)=3 3+(-3)= 4+(-9)= 9+(-)= 7. JEANS The table shows the average price (in dollars) of jeans sold at different stores and the number of pairs of jeans sold at each store in one month. Average Price Number Sold a. Write the ordered pairs from the table and plot them in a coordinate plane. b. Describe the relationship between the two data sets. 8. SUVS The scatter plot shows the numbers of sport utilit vehicles sold in a cit from 9 to 4. a. In what ear were SUVs sold? b. About how man SUVs were sold in 3? c. Describe the relationship shown b the data. Number sold SUV Sales 9 3 Year Earnings of a Food Server Earnings (dollars) Hours worked 9. EARNINGS The scatter plot shows the total earnings (wages and tips) of a food server during one da. a. About how man hours must the server work to earn $7? b. About how much did the server earn for 5 hours of work? c. Describe the relationship shown b the data. 376 Chapter 9 Data Analsis and Displas

8 Describe the relationship between the data. Identif an outliers, gaps, or clusters HONEY The table shows the average price per pound for hone in the United States from 9 to. What tpe of relationship do the data show? Year, 9 Average Price per Pound, $4.65 $4.85 $5.5 $ TEST SCORES The scatter plot shows the numbers of minutes spent studing and the test scores for a science class. (a) What tpe of relationship do the data show? (b) Interpret the relationship. 5. OPEN-ENDED Describe a set of real-life data that has a negative linear relationship. Stud Time and Test Scores Test scores Stud time (minutes) 6. PROBLEM SOLVING The table shows the memor capacities (in gigabtes) and prices (in dollars) of 7-inch tablet computers at a store. (a) Make a scatter plot of the data. Then describe the relationship between the data. (b) Identif an outliers, gaps, or clusters. Eplain wh ou think the eist. Memor (GB), Price (dollars), Sales of sunglasses and beach towels at a store show a positive linear relationship in the summer. Does this mean that the sales of one item cause the sales of the other item to increase? Eplain. Use a graph to solve the equation. Check our solution. (Section 5.4) 8. 5 = = = 3 4. MULTIPLE CHOICE When graphing a proportional relationship represented b = m, which point is not on the graph? (Section 4.3) A (, ) B (, m) C (, m) D (, m) Section 9. Scatter Plots 377

9 9. Lines of Fit How can ou use data to predict an event? ACTIVITY: Representing Data b a Linear Equation Work with a partner. You have been working on a science project for 8 months. Each month, ou measured the length of a bab alligator. The table shows our measurements. September April Month, Length (in.), COMMON CORE Use the following steps to predict the bab alligator s length net September Data Analsis In this lesson, ou will find lines of fit. use lines of fit to solve problems. Learning Standards 8.SP. 8.SP. 8.SP.3 a. Graph the data in the table. b. Draw a line that ou think best approimates the points. c. Write an equation for our line. d. MODELING Use the equation to predict the bab alligator s length net September. Length (inches) Month 378 Chapter 9 Data Analsis and Displas

10 ACTIVITY: Representing Data b a Linear Equation Work with a partner. You are a biologist and stud bat populations. You are asked to predict the number of bats that will be living in an abandoned mine after 3 ears. To start, ou find the number of bats that have been living in the mine during the past 8 ears. The table shows the results of our research. Math Practice Use a Graph How can ou draw a line that fits the collection of points? How should the points be positioned around the line? Year, Bats (thousands), Use the following steps to predict the number of bats that will be living in the mine after 3 ears. a. Graph the data in the table. 7 ears ago this ear b. Draw a line that ou think best approimates the points. c. Write an equation for our line. d. MODELING Use the equation to predict the number of bats in 3 ears. Bats (thousands) Year 3. IN YOUR OWN WORDS How can ou use data to predict an event? 4. MODELING Use the Internet or some other reference to find data that appear to have a linear pattern. List the data in a table, and then graph the data. Use an equation that is based on the data to predict a future event. Use what ou learned about lines of fit to complete Eercise 4 on page 38. Section 9. Lines of Fit 379

11 9. Lesson Lesson Tutorials Ke Vocabular line of fit, p. 38 line of best fit, p. 38 A line of fit is a line drawn on a scatter plot close to most of the data points. It can be used to estimate data on a graph. Month, Stud Tip EXAMPLE Depth (feet), A line of fit does not need to pass through an of the data points. Finding a Line of Fit The table shows the depth of a river months after a monsoon season ends. (a) Make a scatter plot of the data and draw a line of fit. (b) Write an equation of the line of fit. (c) Interpret the slope and the -intercept of the line of fit. (d) Predict the depth in month 9. a. Plot the points in a coordinate plane. The scatter plot shows a negative linear relationship. Draw a line that is close to the data points. Tr to have as man points above the line as below it. b. The line passes through (5, ) and (6, 8). slope = rise run = = Because the line crosses the -ais at (, ), the -intercept is. So, an equation of the line of fit is = +. c. The slope is, and the -intercept is. So, the depth of the river is feet at the end of the monsoon season and decreases b about feet per month. d. To predict the depth in month 9, substitute 9 for in the equation of the line of fit. = + = (9) + = Depth (feet) The depth in month 9 should be about feet. River Depth (5, ) (6, 8) Month Eercises 5 and 6. The table shows the numbers of people who have attended a festival over an 8-ear period. (a) Make a scatter plot of the data and draw a line of fit. (b) Write an equation of the line of fit. (c) Interpret the slope and the -intercept of the line of fit. (d) Predict the number of people who will attend the festival in ear. Year, Attendance, Chapter 9 Data Analsis and Displas

12 Stud Tip You know how to use two points to find an equation of a line of fit. When finding an equation of the line of best fit, ever point in the data set is used. Graphing calculators use a method called linear regression to find a precise line of fit called a line of best fit. This line best models a set of data. A calculator often gives a value r called the correlation coefficient. This value tells whether the correlation is positive or negative, and how closel the equation models the data. Values of r range from to. When r is close to or, there is a strong correlation between the variables. As r gets closer to, the correlation becomes weaker. r r r Strong negative correlation No correlation Strong positive correlation EXAMPLE Finding a Line of Best Fit Using Technolog The table shows the worldwide movie ticket sales (in billions of dollars) from to, where = represents the ear. Use a graphing calculator to find an equation of the line of best fit. Identif and interpret the correlation coefficient. Year, Ticket Sales, Step : Enter the data from the table into our calculator. Step : Use the linear regression feature. slope -intercept Stud Tip The slope of.5 indicates that sales are increasing b about $.5 billion each ear. The -intercept of 6 represents the ticket sales of $6 billion for. Check An equation of the line of best fit is = The correlation coefficient is about.98. This means that the relationship between ears and ticket sales is a strong positive correlation and that the equation closel models the data. Use a graphing calculator to make a scatter plot and graph the line of best fit. 45 correlation coefficient Eercises 8. Use a graphing calculator to find an equation of the line of best fit for the data in Eample. Identif and interpret the correlation coefficient. Section 9. Lines of Fit 38

13 9. Eercises Help with Homework. WRITING Eplain wh a line of fit is helpful when analzing data.. REASONING Tell whether the line drawn on the graph is a good fit for the data. Eplain our reasoning. 3. NUMBER SENSE Which correlation coefficient indicates a stronger relationship:.98 or.9? Eplain. 9+(-6)=3 3+(-3)= 4+(-9)= 9+(-)= 4. BLUEBERRIES The table shows the weights of pints of blueberries. Number of Pints, Weight (pounds), a. Graph the data in the table. b. Draw a line that ou think best approimates the points. c. Write an equation for our line. d. Use the equation to predict the weight of pints of blueberries. e. Blueberries cost $.5 per pound. How much do pints of blueberries cost? 5. HOT CHOCOLATE The table shows the dail high temperature ( F) and the number of hot chocolates sold at a coffee shop for eight randoml selected das. Temperature ( F), Hot Chocolates, a. Make a scatter plot of the data and draw a line of fit. b. Write an equation of the line of fit. c. Interpret the slope and the -intercept of the line of fit. d. Predict the number of hot chocolates sold when the high temperature is F. 6. VACATION The table shows the distance ou are awa from home over a 6-hour period of our vacation. a. Make a scatter plot of the data and draw a line of fit. b. Write an equation of the line of fit. c. About how man miles per hour do ou travel? d. About how far were ou from home when ou started? e. Predict the distance from home in 7 hours. Hours, Distance (miles), Chapter 9 Data Analsis and Displas

14 7. REASONING A data set has no relationship. Is it possible to find a line of fit for the data? Eplain. 8. AMUSEMENT PARK The table shows the attendance (in thousands) at an amusement park from 4 to 3, where = 4 represents the ear 4. Use a graphing calculator to find an equation of the line of best fit. Identif and interpret the correlation coefficient. Year, Attendance (thousands), SNOWSTORM The table shows the total snow depth (in inches) on the ground during a snowstorm hours after it began. Use a graphing calculator to find an equation of the line of best fit. Identif and interpret the correlation coefficient. Use our equation to estimate how much snow was on the ground before the snowstorm began. Hours, Snow Depth (inches), TEXTING The table shows the numbers (in billions) of tet messages sent from 6 to, where = 6 represents the ear 6. a. Use a graphing calculator to find an equation of the line of best fit. Identif and interpret the correlation coefficient. b. Interpret the slope of the line of best fit. Does the -intercept make sense for this problem? Eplain. c. Predict the number of tet messages sent in 5. Year, Tet Messages (billions), Modeling The table shows the height (in feet) of a baseball seconds after it was hit. a. Use a graphing calculator to find an equation of the line of best fit. Identif and interpret the correlation coefficient. b. Predict the height after 5 seconds. c. The actual height after 5 seconds is about 3 feet. Wh do ou think this is different from our prediction? Seconds, Height (feet), Write the decimal as a fraction or a mied number. (Section 7.4) MULTIPLE CHOICE Which epression represents the volume of a sphere with radius r? (Section 8.3) A 3 πr h B πr h C 4πr D 4 3 πr 3 Section 9. Lines of Fit 383

15 9. 9. Quiz Progress Check. CHARITY The scatter plot shows the amount of mone donated to a charit from 7 to. (Section 9.) a. In what ear did the charit receive $5,? b. How much did the charit receive in? c. Describe the relationship shown b the data. Describe the relationship between the data. Identif an outliers, gaps, or clusters. (Section 9.) Donations (thousands of dollars) Donations to Charit Year Year, Millions of Customers, CUSTOMERS SERVED The table shows the numbers of customers (in millions) served b a restaurant chain over an 8-ear period. (Section 9. and Section 9.) a. Make a scatter plot of the data. Then describe the relationship between the data. Identif an outliers, gaps, or clusters. b. Use a graphing calculator to find the equation of the line of best fit for the data. Identif and interpret the correlation coefficient. 6. CATS An animal shelter opens in December. The table shows the number of cats adopted from the shelter each month from Januar to September. (Section 9.) Month Cats a. Make a scatter plot of the data and draw a line of fit. b. Write an equation of the line of fit. c. Interpret the slope and the -intercept of the line of fit. d. Predict how man cats will be adopted in October. Sections Quiz 385

16 9.3 Two-Wa Tables Two categories of data can be displaed in a two-wa table. How can ou read and make a two-wa table? ACTIVITY: Reading a Two-Wa Table Work with a partner. You are the manager of a sports shop. The two-wa table shows the numbers of soccer T-shirts that our shop has left in stock at the end of the season. Color T-Shirt Size S M L XL XXL Total Blue/White 5 4 Blue/Gold Red/White Black/White 3 4 Black/Gold 5 3 Total 65 a. Complete the totals for the rows and columns. b. Are there an black-and-gold XL T-shirts in stock? Justif our answer. c. The numbers of T-shirts ou ordered at the beginning of the season are shown below. Complete the two-wa table. COMMON ON CORE Data Analsis In this lesson, ou will read two-wa tables. make and interpret two-wa tables. Learning Standard 8.SP.4 Color T-Shirt Size S M L XL XXL Total Blue/White Blue/Gold Red/White Black/White Black/Gold Total d. REASONING How would ou alter the numbers of T-shirts ou order for net season? Eplain our reasoning. 386 Chapter 9 Data Analsis and Displas

17 ACTIVITY: Analzing Data Math Practice Construct Arguments What are the advantages of using a table instead of a graph to analze data? Work with a partner. The three-dimensional two-wa table shows information about the numbers of hours students at a high school work at part-time jobs during the school ear. 6 Part-Time Jobs 4 Number of students Bos Girls hours per week 7 hours per week 8+ hours per week a. Make a two-wa table showing the data. Use estimation to find the entries in our table. b. Write two observations ou can make that summarize the data in our table. c. REASONING A newspaper article claims that more bos than girls drop out of high school to work full-time. Do the data support this claim? Eplain our reasoning. 3. IN YOUR OWN WORDS How can ou read and make a two-wa table? 4. Find a real-life data set that ou can represent b a two-wa table. Then make a two-wa table for the data set. Use what ou learned about two-wa tables to complete Eercises 3 6 on page 39. Section 9.3 Two-Wa Tables 387

18 9.3 Lesson Lesson Tutorials Ke Vocabular two-wa table, p. 388 joint frequenc, p. 388 marginal frequenc, p. 388 A two-wa table displas two categories Student of data collected from the same source. Studied Did Not Stud You randoml surve students in our school about their grades on the last test and whether the studied for the test. The two-wa table shows our results. Each entr in the table is called a joint frequenc. Passed Failed joint frequenc 6 Grade EXAMPLE Reading a Two-Wa Table How man of the students in the surve above studied for the test and passed? The entr in the Studied column and Passed row is. So, of the students in the surve studied for the test and passed. The sums of the rows and columns in a two-wa table are called marginal frequencies. EXAMPLE Finding Marginal Frequencies Find and interpret the marginal frequencies for the surve above. Create a new column and a new row for the sums. Then add the entries. Grade Student Studied Did Not Stud Total Passed 3 Failed students passed. 7 students failed. students studied. Total students were surveed. 8 students did not stud. Eercises 5 8. You randoml surve students in a cafeteria about their plans for a football game and a school dance. The two-wa table shows our results. a. How man students will attend the dance but not the football game? b. Find and interpret the marginal frequencies for the surve. Dance Football Game Attend Not Attend Attend 35 5 Not Attend Chapter 9 Data Analsis and Displas

19 EXAMPLE Rides Bus Age Tall Making a Two-Wa Table You randoml surve students between the ages of and 7 about whether the ride the bus to school. The results are shown in the tall sheets. Make a two-wa table that includes the marginal frequencies. The two categories for the table are the ages and whether or not the ride the bus. Use the tall sheets to calculate each joint frequenc. Then add to find each marginal frequenc. Does Not Ride Bus Age Tall Student Age Total Rides Bus Does Not Ride Bus Total EXAMPLE 4 Finding a Relationship in a Two-Wa Table Use the two-wa table in Eample 3. a. For each age group, what percent of the students in the surve ride the bus to school? do not ride the bus to school? Organize the results in a two-wa table. Eplain what one of the entries represents. Student Age Rides Bus 6% 48% 4% Does Not Ride Bus 4% 5% 6% 4 35 =.4 So, 4% of the 6- and 7-ear-old students in the surve ride the bus to school. b. Does the table in part (a) show a relationship between age and whether students ride the bus to school? Eplain. Yes, the table shows that as age increases, students are less likel to ride the bus to school. Eercise Grade 6 Students pack lunch, 9 bu school lunch Grade 7 Students 3 pack lunch, 7 bu school lunch Grade 8 Students 6 pack lunch, 4 bu school lunch. You randoml surve students in a school about whether the bu a school lunch or pack a lunch. Your results are shown. a. Make a two-wa table that includes the marginal frequencies. b. For each grade level, what percent of the students in the surve pack a lunch? bu a school lunch? Organize the results in a two-wa table. Eplain what one of the entries represents. c. Does the table in part (b) show a relationship between grade level and lunch choice? Eplain. Section 9.3 Two-Wa Tables 389

20 9.3 Eercises Help with Homework. VOCABULARY Eplain the relationship between joint frequencies and marginal frequencies.. OPEN-ENDED Describe how ou can use a two-wa table to organize data ou collect from a surve. 9+(-6)=3 3+(-3)= 4+(-9)= 9+(-)= You randoml surve students about participating in their class s earl fundraiser. You displa the two categories of data in the two-wa table. 3. Find the total of each row. 4. Find the total of each column. 5. How man female students will be participating in the fundraiser? 6. How man male students will not be participating in the fundraiser? Gender Fundraiser No Yes Female 5 Male 3 9 Find and interpret the marginal frequencies. 7. Class School Pla Attend Not Attend Junior 4 3 Senior Cell Phone Minutes Limited Unlimited Tet Plan Limited 78 Unlimited GOALS You randoml surve students in our school. You ask what is most important to them: grades, popularit, or sports. You displa our results in the two-wa table. a. How man 7th graders chose sports? How man 8th graders chose grades? b. Find and interpret the marginal frequencies for the surve. c. What percent of students in the surve are 6th graders who chose popularit? Grade Goal Grades Popularit Sports 6th th th Chapter 9 Data Analsis and Displas

21 3 4. SAVINGS You randoml surve people in our neighborhood about whether the have at least $ in savings. The results are shown in the tall sheets. a. Make a two-wa table that includes the marginal frequencies. b. For each age group, what percent of the people have at least $ in savings? do not have at least $ in savings? Organize the results in a two-wa table. c. Does the table in part (b) show a relationship between age and whether people have at least $ in savings? Eplain.. EYE COLOR You randoml surve students in our school about the color of their ees. The results are shown in the tables. Have at Least $ in Savings Age Tall Don t Have at Least $ in Savings Age Tall Ee Color of Males Surveed Green Blue Brown Ee Color of Females Surveed Green Blue Brown a. Make a two-wa table. b. Find and interpret the marginal frequencies for the surve. c. For each ee color, what percent of the students in the surve are male? female? Organize the results in a two-wa table. Eplain what two of the entries represent.. REASONING Use the information from Eercise. For each gender, what percent of the students in the surve have green ees? blue ees? brown ees? Organize the results in a two-wa table. Eplain what two of the entries represent. 3. Precision What percent of students in the surve in Eercise are either female or have green ees? What percent of students in the surve are males who do not have green ees? Find and eplain the sum of these two percents. Write an equation of the line that passes through the points. (Section 4.6) 4. (, ), (, 5) 5. (, ), (3, 3) 6. ( 4, ), (, 3) 7. MULTIPLE CHOICE Which equation does not represent a linear function? (Section 6.4) A = 4 B = 8 C = 3 D = Section 9.3 Two-Wa Tables 39

22 9.4 Choosing a Data Displa ou make decisions? How can ou displa data in a wa that helps ACTIVITY: Displaing Data Work with a partner. Analze and displa each data set in a wa that best describes the data. Eplain our choice of displa. a. ROADKILL A group of schools in New England participated in a -month stud. The reported 396 dead animals. Birds: 37 Mammals: 746 Amphibians: 45 Reptiles: 75 Unknown: 689 b. BLACK BEAR ROADKILL The data below show the numbers of black bears killed on a state s roads from 993 to. 993: 3 994: : : : : : 43 : 47 : 49 : 6 3: 74 4: 88 5: 8 6: 9 7: 99 8: 9 9: : 7 : 4 : 35 COMMON CORE Data Analsis In this lesson, ou will choose appropriate data displas. identif and analze misleading data displas. Appling Standard 8.SP. c. RACCOON ROADKILL A -week stud along a 4-mile section of road found the following weights (in pounds) of raccoons that had been killed b vehicles d. What do ou think can be done to minimize the number of animals killed b vehicles? 39 Chapter 9 Data Analsis and Displas

23 ACTIVITY: Statistics Project Math Practice Use a Graph How can ou use a graph to represent the data ou have gathered for our report? What does the graph tell ou about the data? ENDANGERED SPECIES PROJECT Use the Internet or some other reference to write a report about an animal species that is (or has been) endangered. Include graphical displas of the data ou have gathered. Sample: Florida Ke Deer In 939, Florida banned the hunting of Ke deer. The numbers of Ke deer fell to about in the 94s. In 947, public sentiment was stirred b -ear-old Glenn Allen from Miami. Allen organized Bo Scouts and others in a letterwriting campaign that led to the establishment of the National Ke Deer Refuge in 957. The approimatel 86-acre refuge includes 8 acres of designated wilderness. The Ke Deer Refuge has increased the population of Ke deer. A recent stud estimated the total Ke deer population to be approimatel 8. About half of Ke deer deaths are due to vehicles. One of two Ke deer wildlife underpasses on Big Pine Ke 3. IN YOUR OWN WORDS How can ou displa data in a wa that helps ou make decisions? Use the Internet or some other reference to find eamples of the following tpes of data displas. Bar graph Circle graph Scatter plot Stem-and-leaf plot Bo-and-whisker plot Use what ou learned about choosing data displas to complete Eercise 3 on page 397. Section 9.4 Choosing a Data Displa 393

24 9.4 Lesson Lesson Tutorials Data Displa Pictograph What does it do? shows data using pictures A B C D Bar Graph shows data in specific categories Circle Graph Line Graph Histogram shows data as parts of a whole shows how data change over time shows frequencies of data values in intervals of the same size Stem-and-Leaf Plot Bo-and-Whisker Plot orders numerical data and shows how the are distributed shows the variabilit of a data set b using quartiles Dot Plot shows the number of times each value occurs in a data set Scatter Plot shows the relationship between two data sets b using ordered pairs in a coordinate plane EXAMPLE Choosing an Appropriate Data Displa Choose an appropriate data displa for the situation. Eplain our reasoning. a. the number of students in a marching band each ear A line graph shows change over time. So, a line graph is an appropriate data displa. b. a comparison of people s shoe sizes and their heights You want to compare two different data sets. So, a scatter plot is an appropriate data displa. Eercises 4 7 Choose an appropriate data displa for the situation. Eplain our reasoning.. the population of the United States divided into age groups. the percents of students in our school who pla basketball, football, soccer, or lacrosse 394 Chapter 9 Data Analsis and Displas

25 EXAMPLE Identifing an Appropriate Data Displa You record the number of hits for our school s new website for 5 months. Tell whether the data displa is appropriate for representing how the number of hits changed during the 5 months. Eplain our reasoning. a. Website Hits Month Hits August 5 September 3 October 485 November 65 December 95 Number of hits Aug Sep Oct Nov Month The bar graph shows the number of hits for each month. So, it is an appropriate data displa. Dec b. Website Hits Frequenc Number of hits The histogram does not show the number of hits for each month or how the number of hits changes over time. So, it is not an appropriate data displa. c. Website Hits Number of hits Aug Sep Oct Nov Dec Month The line graph shows how the number of hits changes over time. So, it is an appropriate data displa. Eercises 8 and 9 Tell whether the data displa is appropriate for representing the data in Eample. Eplain our reasoning. 3. dot plot 4. circle graph 5. stem-and-leaf plot Section 9.4 Choosing a Data Displa 395

26 EXAMPLE Identifing a Misleading Data Displa 3 Which line graph is misleading? Eplain. Bo Office Revenue Total revenue (billions of dollars) Total revenue (billions of dollars) Bo Office Revenue Year Year The vertical ais of the line graph on the left has a break ( ) and begins at 8. This graph makes it appear that the total revenue increased rapidl from 5 to 9. The graph on the right has an unbroken ais. It is more honest and shows that the total revenue increased slowl. So, the graph on the left is misleading. EXAMPLE Analzing a Misleading Data Displa 4 A volunteer concludes that the numbers of cans of food and boes of food donated were about the same. Is this conclusion accurate? Eplain. Food Drive Donation Totals Canned food Each icon represents the same number of items. Because the bo icon is larger than the can icon, it looks like the number of boes is about the same as the number of cans. But the number of boes is actuall about half of the number of cans. Boed food Juice â cans â boes â bottles So, the conclusion is not accurate. Eplain wh the data displa is misleading. Eercises Compan Profits Profit (billions of dollars) Concert ticket price (dollars) Concert Ticket Prices A B Rock band 396 Chapter 9 Data Analsis and Displas C Year 4 5

27 Eercises 9.4 Help with Homework. REASONING Can more than one displa be appropriate for a data set? Eplain.. OPEN-ENDED Describe how a histogram can be misleading. 6)=3 9+(- 3)= 3+(- 9)= 4+(- = ) 9+(- 3. Analze and displa the data in a wa that best describes the data. Eplain our choice of displa. Notebooks Sold in One Week 9 red 7 green 65 ellow purple 3 black 83 pink 3 blue 5 orange 79 white 8 other Choose an appropriate data displa for the situation. Eplain our reasoning. 4. a student s test scores and how the scores are spread out 5. the distance a person drives each month 6. the outcome of rolling a number cube 7. homework problems assigned each da 8. LIFEGUARD The table shows how man hours ou worked as a lifeguard from Ma to August. Tell whether the data displa is appropriate for representing how the number of hours worked changed during the 4 months. Eplain our reasoning. a. Lifeguard Schedule Month Hours Worked Ma 4 June 8 Jul 6 August Ma June Jul August â hours Ke: b. Lifeguard Schedule Hours worked Ma June Jul August Month Section 9.4 Choosing a Data Displa 397

28 9. FAVORITE SUBJECT A surve asked 8 students to choose their favorite subject. The results are shown in the table. Tell whether the data displa is appropriate for representing the portion of students who prefer math. Eplain our reasoning. a. b. Favorite School Subject Favorite School Subject Subject Number of Students Science Math 6 Literature 4 Social Studies Other 8 Favorite School Subject Science 5% Math % Literature 3% Social Studies 5% Other % Number of students Science Math Literature Social Studies Subject Other. WRITING When should ou use a histogram instead of a bar graph to displa data? Use an eample to support our answer. Eplain wh the data displa is misleading Miles Biked. Monthl Sales Monda Tuesda Wednesda mile Sales (millions of dollars) April Ma June Jul Month 3. Miles Walked 4. Monthl Rainfall Frequenc Miles Rainfall (inches) Januar Februar March April Month 398 Chapter 9 Data Analsis and Displas

29 5. VEGETABLES A nutritionist wants to use a data displa to show the favorite vegetables of the students at a school. Choose an appropriate data displa for the situation. Eplain our reasoning. 6. CHEMICALS A scientist gathers data about a decaing chemical compound. The results are shown in the scatter plot. Is the data displa misleading? Eplain. 7. REASONING What tpe of data displa is appropriate for showing the mode of a data set? 8. SPORTS A surve asked students to choose their favorite sports. The results are shown in the circle graph. a. Eplain wh the graph is misleading. b. What tpe of data displa would be more appropriate for the data? Eplain. Grams Favorite Sports Soccer 35% Football 6% Decaing Chemical Compound,, Hours Basketball 3% Racquetball 5% Other 4% 9. With the help of computers, mathematicians have computed and analzed billions of digits of the irrational number π. One of the things the analze is the frequenc of each of the numbers through 9. The table shows the frequenc of each number in the first, digits of π. a. Displa the data in a bar graph. b. Displa the data in a circle graph. c. Which data displa is more appropriate? Eplain. d. Describe the distribution. Number Frequenc 9999,37 998,5 997,6,9, Estimate the square root to the nearest (a) integer and (b) tenth. (Section 7.4) MULTIPLE CHOICE What is % of 5% of 4? (Skills Review Handbook) A B C 4 D 38 Section 9.4 Choosing a Data Displa 399

30 Quiz Progress Check. RECYCLING The results of a reccling surve are shown in the two-wa table. Find and interpret the marginal frequencies. (Section 9.3). MUSIC The results of a music surve are shown in the two-wa table. Find and interpret the marginal frequencies. (Section 9.3) Reccle Jazz Yes No Likes Dislikes Gender Female 8 9 Male 4 4 Countr Likes 6 4 Dislikes ELECTION The results of a voting surve are shown in the two-wa table. (Section 9.3) a. Find and interpret the marginal frequencies. b. For each age group, what percent of voters prefer Smith? prefer Jackson? Organize our results in a two-wa table. Candidate Voter s Age Smith Jackson 3 4 c. Does our table in part (b) show a relationship between age and candidate preference? Eplain. Choose an appropriate data displa for the situation. Eplain our reasoning. (Section 9.4) 4. the percent of band students in each section of instruments 5. a compan s profit for each week 6. TURTLES The tables show the weights (in pounds) of turtles caught in two ponds. Which tpe of data displa would ou use for this information? Eplain. (Section 9.4) Pond A Pond B Funds Raised for Class Trip Amount raised (dollars) Month 7. FUNDRAISER The line graph shows the amount of mone that the eighth-grade students at a school raised each month to pa for a class trip. Is the graph misleading? Eplain. (Section 9.4) 4 Chapter 9 Data Analsis and Displas

31 9 Chapter Review Vocabular Help Review Ke Vocabular scatter plot, p. 374 line of fit, p. 38 line of best fit, p. 38 two-wa table, p. 388 joint frequenc, p. 388 marginal frequenc, p. 388 Review Eamples and Eercises 9. Scatter Plots (pp ) Your school is ordering custom T-shirts. The scatter plot shows the number of T-shirts ordered and the cost per shirt. What tends to happen to the cost per shirt as the number of T-shirts ordered increases? Looking at the graph, the plotted points go down from left to right. So, as the number of T-shirts ordered increases, the cost per shirt decreases. Cost per T-shirt (dollars) Custom T-Shirts T-shirts ordered. MIGRATION The scatter plot shows the number of geese that migrated to a park each season. a. In what ear did 7 geese migrate? b. How man geese migrated in? c. Describe the relationship shown b the data. Describe the relationship between the data. Identif an outliers, gaps, or clusters. Number of geese Geese Migration to a Park Year Chapter Review 4

32 9. Lines of Fit (pp ) The table shows the revenue (in millions of dollars) for a compan over an 8-ear period. (a) Make a scatter plot of the data and draw a line of fit. (b) Write an equation of the line of fit. (c) Interpret the slope and the -intercept of the line of fit. (d) Predict what the revenue will be in ear 9. Year, Revenue (millions of dollars), a. Plot the points in a coordinate plane. The scatter plot shows a positive linear relationship. Draw a line that is close to the data points. b. slope = rise run = 36 3 = Because the line crosses the -ais at (, 8), the -intercept is 8. So, an equation of the line of fit is = + 8. Revenue (millions of dollars) 8 Revenue 5 9 (6, 8) (3, 46) Year c. The slope is. So, the revenue increased b about $ million each ear. The -intercept is 8. So, ou can estimate that the revenue was $8 million in the ear before this 8-ear period. d. = + 8 = (9) + 8 = 6 The revenue in ear 9 will be about $6 million. 5. STUDENTS The table shows the number of students at a middle school over a -ear period. a. Make a scatter plot of the data and draw a line of fit. b. Write an equation of the line of fit. c. Interpret the slope and the -intercept of the line of fit. d. Predict the number of students in ear. 6. LINE OF BEST FIT Use a graphing calculator to find an equation of the line of best fit for the data in Eercise 5. Identif and interpret the correlation coefficient. Year, Number of Students, Chapter 9 Data Analsis and Displas

33 9.3 Two-Wa Tables (pp ) You randoml surve students in our school about whether the liked a recent school pla. The results are shown. Make a two-wa table that includes the marginal frequencies. What percent of the students surveed liked the pla? Of the 3 students surveed, 4 students liked the pla. 4 Because =.8, 8% of the 3 students in the surve liked the pla. Gender Male Students 48 likes, dislikes Female Students 56 likes, 4 dislikes Student Liked Did Not Like Total Male 48 6 Female Total You randoml surve people at a mall about whether the like the new food court. The results are shown. 7. Make a two-wa table that includes the marginal frequencies. 8. For each group, what percent of the people surveed like the food court? dislike the food court? Organize our results in a two-wa table. 9. Does our table in Eercise 8 show a relationship between age and whether people like the food court? Teenagers 96 likes, 4 dislikes Adults likes, 79 dislikes Senior Citizens 8 likes, 8 dislikes 9.4 Choosing a Data Displa (pp ) Choose an appropriate data displa for the situation. Eplain our reasoning. a. the percent of votes that each candidate received in an election A circle graph shows data as parts of a whole. So, a circle graph is an appropriate data displa. b. the distribution of the ages of U.S. presidents A stem-and-leaf plot orders numerical data and shows how the are distributed. So, a stem-and-leaf plot is an appropriate data displa. Choose an appropriate data displa for the situation. Eplain our reasoning.. the number of pairs of shoes sold b a store each week. a comparison of the heights of brothers and sisters Chapter Review 43

34 9 Stud Help Graphic Organizer You can use an information frame to help ou organize and remember concepts. Here is an eample of an information frame for scatter plots. Eample: Positive Linear Relationship Words: A scatter plot shows the relationship between two data sets using ordered pairs in a coordinate plane. Eample: Negative Linear Relationship O The points lie close to a line. As increases, increases. Scatter Plots Eamples: Nonlinear No Relationship Relationship O The points lie close to a line. As increases, decreases. O The points lie in the shape of a curve. O The points show no pattern. Make an information frame to help ou stud this topic.. lines of fit After ou complete this chapter, make information frames for the following topics.. two-wa tables 3. data displas Dear Teacher, I am ing m information frame showing the characteristics of circles. 384 Chapter 9 Data Analsis and Displas

35 9 Chapter Test Test Practice. POPULATION The graph shows the population (in millions) of the United States from 96 to. a. In what ear was the population of the United States about 8 million? b. What was the approimate population of the United States in 99? c. Describe the trend shown b the data. Population (millions) U.S. Population Year. WEIGHT The table shows the weight of a bab over several months. a. Make a scatter plot of the data and draw a line of fit. b. Write an equation of the line of fit. c. Interpret the slope and the -intercept of the line of fit. d. Predict how much the bab will weigh at 7 months. Age (months) Weight (pounds) Fiction Nonfiction Likes Dislikes Likes 6 Dislikes 3. READING You randoml surve students at our school about what tpe of books the like to read. The two-wa table shows our results. Find and interpret the marginal frequencies. Choose an appropriate data displa for the situation. Eplain our reasoning. 4. magazine sales grouped b price 5. the distance a person hikes each week 6. SAT The table shows the numbers of students (in thousands) who took the SAT from 6 to, where = 6 represents the ear 6. Use a graphing calculator to find an equation of the line of best fit. Identif and interpret the correlation coefficient. Year, Number of Students, RECYCLING You randoml surve shoppers at a supermarket about whether the use reusable bags. Of 6 male shoppers, 5 use reusable bags. Of female shoppers, 6 use reusable bags. Organize our results in a two-wa table. Include the marginal frequencies. 44 Chapter 9 Data Analsis and Displas

36 9 Standards Assessment. What is the volume of the trash bin? (8.G.9) Test-Taking Strateg Read All Choices Before Answering 6 in. in. A. 88π in. 3 C. 648π in. 3 B. 576π in. 3 D. 7π in. 3. The diagram below shows parallel lines cut b a transversal. Which angle is the corresponding angle for 6? (8.G.5) Reading all choices before answering can sometimes point out the obvious answer! F. H. 4 G. 3 I You randoml surve students in our school. You ask whether the have jobs. You displa our results in the two-wa table. How man male students do not have a job? (8.SP.4) Yes Job No Gender Male 7 Female 3 7 Standards Assessment 45

37 4. Which scatter plot shows a negative relationship between and? (8.SP.) A C B D The legs of a right triangle have the lengths of 8 centimeters and 5 centimeters. What is the length of the hpotenuse, in centimeters? (8.G.7) 6. What is the solution of the equation? (8.EE.7b).( + 6) =. +.8 F. =.4 H. = 4 G. = 5.6 I. = Which triangle is not a right triangle? (8.G.6) A. 4 cm cm C. 3 in. 6 cm 9 in. 6 in. B. 53 m D. 5 ft 8 m 45 m 45 ft 4 ft 46 Chapter 9 Data Analsis and Displas

38 8. A store has recorded total dollar sales each month for the past three ears. Which tpe of graph would best show how sales have increased over this time period? (8.SP.) F. circle graph H. histogram G. line graph I. stem-and-leaf plot 9. Trapezoid KLMN is graphed in the coordinate plane shown. K L O 3 4 N 4 M Rotate Trapezoid KLMN 9 clockwise about the origin. What are the coordinates of point M, the image of point M after the rotation? (8.G.3) A. ( 3, ) C. (, 3) B. (, 3) D. (3, ). The table shows the numbers of hours students spent watching television from Monda through Frida for one week and their scores on a test that Frida. (8.SP., 8.SP.) Hours of Television, Test Score, Part A Part B Part C Make a scatter plot of the data. Describe the relationship between hours of television watched and test score. Eplain how to justif our answer in Part B using the linear regression feature of a graphing calculator. Standards Assessment 47