Lesson 15.1 Skills Practice

Lesson 15.1 Skills Practice Name Date School Spirit and Scatter Plots Using Scatter Plots to Display and Analyze Two-Variable Relationships Vocabulary Write a definition for each term in your own words. 1. scatter plot The graph of a set of ordered pairs. 2. two-variable data set A data set that includes two separate characteristics about the same person or thing. 3. variable The specific characteristic of the information gathered when collecting information about a person or thing. Chapter 15 Skills Practice 955

Lesson 15.1 Skills Practice page 2 Problem Set Construct a scatter plot or create a table of values for each data set. Describe any pattern you observe. Circle the third point from the table on the graph and explain what it means. 1. Emma and Linnea, the managers of the girls basketball team, have collected information on the average points scored by each player and the average minutes played by each player. Average Minutes Played 1 2 15 12 5 8 12 14 9 16 6 3 Average Points Scored 7 14 1 8 3 5 9 9 7 12 4 1 y Average Minutes Played vs. Average Points Scored Average Points Scored 18 16 14 12 1 8 6 4 2 x 5 1 15 2 Average Minutes Played The average points scored seems to increase as the average minutes played increases. The point (15, 1) means that the average minutes played by one player is 15 minutes and that same player s average points scored is 1 points. 956 Chapter 15 Skills Practice

Lesson 15.1 Skills Practice page 3 Name Date 2. A grocery store tracks the number of gallons of milk it sells each day and the daily price charged for each gallon. Number of Gallons Sold 12 9 14 13 8 1 11 15 7 Price per Gallon ($) 2.75 3.3 2.25 2.5 3.5 3.25 3. 2. 3.55 y Number of Gallons Sold vs. Price per Gallon 4.5 Price per Gallon ($) 4. 3.5 3. 2.5 2. 1.5 7 9 11 13 15 17 19 21 22 Number of Gallons Sold x The price charged per gallon of milk seems to decrease as the number of gallons sold increases. The point (14, 2.25) means that when 14 gallons of milk are sold in a day, the price per gallon is $2.25. Chapter 15 Skills Practice 957

Lesson 15.1 Skills Practice page 4 3. A personal trainer tracks the calories burned by his clients for the number of miles they run. Number of Miles Run 3 4.5 5 2.5 7 8 6 5.5 4 Number of Calories Burned 275 475 6 3 85 8 65 525 4 1 9 8 7 Calories Burned 6 5 4 3 2 1 1 2 3 4 5 6 Miles Run 7 8 9 1 The number of calories burned seems to increase with the number of miles run. The point (5, 6) means that a person who ran 5 miles, burned 6 calories. 958 Chapter 15 Skills Practice

Lesson 15.1 Skills Practice page 5 Name Date 4. Jada, a meteorologist, is studying the average temperatures in the month of June for different latitudes in the northern hemisphere. Latitude (degrees) 45 2 6 5 15 25 3 1 5 Average June Temp. ( F) 75 86 5 12 9 84 81 96 68 y Latitude vs. Average Temperature 18 Average Temperature ( F) 16 14 12 1 8 6 4 2 1 2 3 4 5 6 7 8 9 Latitude (degrees) x The average temperature in June seems to decrease as the latitude of the location increases. The point (6, 5) means that at a latitude of 6 the average temperature in June is 5 F. Chapter 15 Skills Practice 959

Lesson 15.1 Skills Practice page 6 5. A mathematics teacher tracked the number of student absences and the students math grades for the year. Number of Absences 3 2 5 1 8 3 2 6 Math Grades (%) 85 9 65 9 1 6 8 95 75 1 9 8 7 Math Grade (%) 6 5 4 3 2 1 1 2 3 4 5 6 7 8 9 1 Number of Absences The students math grades seem to decrease as their number of absences increase. The point (5, 65) means that a student with five absences for the year had a math grade of 65%. 96 Chapter 15 Skills Practice

Lesson 15.1 Skills Practice page 7 Name Date 6. Heather, a local real estate agent, has collected data about the average selling price for an acre of land in her county for various years. Year 199 25 1995 29 2 1998 22 1985 1988 27 Price Per Acre ($) 13 165 12 18 15 135 17 11 125 175 y Year vs. Average Price per Acre 19 Average Price Per Acre ($) 18 17 16 15 14 13 12 11 1985 x 199 1995 2 25 21 Year As the years increase, the average price of land per acre seems to also increase. The point (1995, 12) means that in the year 1995, the price of land per acre was $12. Chapter 15 Skills Practice 961

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Lesson 15.2 Skills Practice Name Date Jump In! The Water s Fine! Interpreting Patterns in Scatter Plots Vocabulary Match each term to its corresponding definition. 1. independent variable (explanatory variable) c a. when points on a scatter plot seem to form a line 2. dependent variable (response variable) f b. when as the independent variable increases the dependent variable also increases. 3. linear association a c. the variable whose value is not determined by another variable 4. cluster e d. a point that varies greatly from the overall pattern of the data 5. positive association b e. when points on a scatter plot are not in a perfect line but are grouped close to an imagined line 6. negative association g f. the variable whose value is determined by an independent variable 7. outlier d g. when the dependent variable decreases as the explanatory variable increases Chapter 15 Skills Practice 963

Lesson 15.2 Skills Practice page 2 Problem Set Identify the dependent and independent variables in each. Determine whether the scatter plot shows an association or not, and if so, tell if it is positive or negative. State the association in terms of the variables. Identify any outliers. 1. A teacher surveyed students about the amount of sleep they got the night before the math test. 1 Sleep and Test Scores 9 8 7 Math Test Score 6 5 4 3 2 1 1 2 3 4 5 6 Hours of Sleep 7 8 9 1 The number of hours of sleep is the independent variable and math test scores is the dependent variable. There is a linear association between the two variables. There is a positive association between the two variables. Students math test scores increase as the hours of sleep received increases. The points (5, 1) and (9.5, 7) are potential outliers. 964 Chapter 15 Skills Practice

Lesson 15.2 Skills Practice page 3 Name Date 2. Suzanne is collecting data for a research paper. She collects the following age and height data for 1 adults. y Age vs. Height 78 76 Height (inches) 74 72 7 68 66 64 62 6 2 x 3 4 5 6 7 Age (years) Age is the independent variable and height is the dependent variable. There does not appear to be a linear association, so it is neither positive nor negative and no outliers can be identified. Chapter 15 Skills Practice 965

Lesson 15.2 Skills Practice page 4 3. Scientists studying the Bermuda Triangle measured the ocean s temperature at various depths. y Depth vs. Temperature 75 7 65 6 55 5 45 4 35 3 5 1 15 x 2 Depth (feet) Temperature ( F) Depth is the independent variable and temperature is the dependent variable. There is a linear association between the two variables. There is a negative association between the two variables. Temperature decreases as depth increases. The point (2, 38) is a potential outlier. 966 Chapter 15 Skills Practice

Lesson 15.2 Skills Practice page 5 Name Date 4. A used car dealership collected data about the age of the cars they sold and the price they sold them for. 2, Used Car Prices 18, 16, 14, 12, Cost ($) 8 6 4 2 1 2 3 4 5 6 Age of Car 7 8 9 1 1, The age of a car is the independent variable and the cost of a car is the dependent variable. There is a linear association between the two variables. There is a negative association between the two variables. The cost of a used car decreases as the age of the car increases. The point (7, 18,) is a potential outlier. Chapter 15 Skills Practice 967

Lesson 15.2 Skills Practice page 6 5. Nathan and Alex, the managers of the boys basketball team, have collected data on the players heights and the average number of points scored by each player. y Height vs. Average Points Scored 18 Average Points Scored 16 14 12 1 8 6 4 2 56 58 6 62 64 66 68 7 72 74 Height (inches) x Height is the independent variable and average points scored is the dependent variable. There does not appear to be a linear association, so it is neither positive nor negative and no outliers can be identified. 968 Chapter 15 Skills Practice

Lesson 15.2 Skills Practice page 7 Name Date 6. Hugo has collected data about the unemployment rate in his county over the last several decades. 11. y Year vs. Unemployment Rate 1.5 1. Unemployment Rate (%) 9.5 9. 8.5 8. 7.5 7. 6.5 6. 5.5 5. 197 1975 198 1985 199 1995 2 25 x 21 Year The year is the independent variable and the unemployment rate is the dependent variable. There does not appear to be a linear association, so it is neither positive nor negative and no outliers can be identified. Chapter 15 Skills Practice 969

Lesson 15.2 Skills Practice page 8 7. A gas station has collected data about the number of gallons of regular unleaded gas it sells each week and the average price charged for each gallon during that week. y Gallons Sold vs. Price per Gallon 3.2 3.1 Price per Gallon ($) 3. 2.9 2.8 2.7 2.6 2.5 2.4 2.3 14 16 18 2 22 24 26 Gallons Sold (thousands) x The number of gallons of gas sold is the independent variable and price per gallon is the dependent variable. There is a linear association between the two variables. There is a negative association between the two variables. Price of gas per gallon decreases as gallons of gas sold increases. There do not appear to be any outliers. 97 Chapter 15 Skills Practice

Lesson 15.2 Skills Practice page 9 Name Date 8. Rayneisha, a department store manager, has collected data on the store s advertising costs for a certain year and the corresponding profit for that year. y Advertising Costs vs. Profit 48 46 Profit (thousands of $) 44 42 4 38 36 34 32 3 4 6 8 1 12 14 16 18 2 22 Advertising Costs (thousands of $) x Advertising costs is the independent variable and profit is the dependent variable. There is a linear association between the two variables. There is a positive association between the two variables. Profit increases as advertising costs increase. The point (2, 41) is a potential outlier. Chapter 15 Skills Practice 971

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Lesson 15.3 Skills Practice Name Date How Fast Are Your Nerve Impulses? Connecting Tables and Scatter Plots for Collected Data Problem Set 1. Students set up an experiment to see if practice really does make perfect. Each student was given a certain number of practice balls to throw into a bucket 25 feet away. Then the student was given five balls to toss into the bucket. The percentage out of those 5 throws was recorded in the table. Three trials of the experiment were performed. Answer each question for the data given in the table. Number of Practice Balls Thrown Trial 1 (%) Trial 2 (%) Trial 3 (%) Average Throw Percentage (%) 2 2 4 27% 1 4 2 4 33% 2 4 6 4 47% 5 8 8 6 73% 1 8 4 1 73% 15 6 8 1 8% 2 1 8 1 93% a. Calculate the average throw percentages. Round averages to the whole percent. Write your answers in the table. b. What is the independent the dependent variable? The number of practice balls thrown is the independent variable. Average throw percentage is the dependent variable. c. Write ordered pairs for the data. Then, create a scatter plot for the data. (, 27); (1, 33); (2, 47); (5, 73); (1, 73); (15, 8); (2, 93) Chapter 15 Skills Practice 973

Lesson 15.3 Skills Practice page 2 1 Practice Throws and Throw Percentage 9 8 Average Throw Percentage (%) 7 6 5 4 3 2 1 2 4 6 8 1 12 14 16 18 2 Number of Practices Balls Thrown d. Does there appear to be a linear association between the dependent and independent variables? State the association in terms of the variables. Yes, there is a linear association. As the number of practice throws increase, the average throw percentage also increases. e. Is there a positive or negative association between the number of practice throws and average throw percentage? There is a positive association between the number of practice throws and the average throw percentage. f. Write the ordered pair for the point on the scatter plot that represents the greatest average throw percentage. Identify the values of the coordinates and what they mean. The point (2, 93) means that after throwing 2 practice throws, the student s average throw percentage was 93%. 974 Chapter 15 Skills Practice

Lesson 15.3 Skills Practice page 3 Name Date g. Write the ordered pair for the point on the scatter plot that represents the least practice balls thrown. Identify the values of the coordinates and what they mean. The point (, 27) means that after throwing practice throws, the student s average throw percentage was 27%. 2. The student council tracked data on various committees that were set up throughout the year to work on different projects. They tracked the size of the committee (the number of committee members) and the average length of their meetings. The data is shown in the scatter plot. Use the scatter plot to answer each question. Average Length of Meeting (min.) 1 9 8 7 6 5 4 3 2 y Committee Meeting Lengths 1 x 2 4 6 8 1 12 14 16 18 2 Number of Committee Members a. Use the data points from the scatter plot to complete the table. Number of Committee Members 3 12 8 2 5 1 5 15 18 Average Meeting Length (min.) 1 25 2 6 15 3 2 35 45 Chapter 15 Skills Practice 975

Lesson 15.3 Skills Practice page 4 b. Does there appear to be a linear association between the dependent and independent variables? State the association in terms of the variables. Yes, there is a linear association. As the number of committee members increases, the average meeting length also increases. c. Is there a positive or negative association between the number of committee members and the average meeting length? There is a positive association between the number of committee members and the average meeting length. d. Write the ordered pair with the greatest number of committee members. Explain the meaning of each of the coordinates. (2, 6); The x-coordinate means that the committee has 2 members. The y-coordinate means that the committee s meetings last an average of 6 minutes. e. Write the ordered pair for the committee with the shortest meetings. Explain where you would find the point on the scatter plot. (3, 1); You would find the point (3, 1) at the lower left corner of the graph as the values of both coordinates are close to. f. Write the ordered pair for the committee with the longest meetings. Explain where you would find the point on the table. (2, 6); You would look for the largest value along the top row. g. Write the ordered pairs for the committees with the same number of members. How many members did they have and how long were each of their average meetings? (5, 15) and (5, 2); Both committees have 5 members and the first has an average meeting length of 15 minutes and the second has an average meeting length of 2 minutes. h. Write the ordered pairs for the committees with the same length of meetings. How long are their meetings and how many members do they each have? (5, 2) and (8, 2); Both committees have an average meeting length of 2 minutes and the first has 5 members and the second has 8 members. 976 Chapter 15 Skills Practice