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
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person or thing.
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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
10
20
15
12
5
8
12
14
9
16
6
3
Average Points Scored
7
14
10
8
3
5
9
9
7
12
4
1
y
Average Minutes Played vs. Average Points Scored
18 Average Points Scored
16 14 12 10 8 6 4 2 0
0
5 10 15 Average Minutes Played
x 20
The point (15, 10) means that the average minutes played by one player is 15 minutes and that same player’s average points scored is 10 points.
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The average points scored seems to increase as the average minutes played increases.
Lesson 15.1 Skills Practice
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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
120
90
140
130
80
100
110
150
70
Price per Gallon ($)
2.75
3.30
2.25
2.50
3.50
3.25
3.00
2.00
3.55
y
Number of Gallons Sold vs. Price per Gallon
Price per Gallon ($)
4.5 4.0 3.5 3.0 2.5 2.0 1.5
70 90 110 130 150 170 190 210 220 Number of Gallons Sold
x
The price charged per gallon of milk seems to decrease as the number of gallons sold
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increases. The point (140, 2.25) means that when 140 gallons of milk are sold in a day, the price per gallon is $2.25.
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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
600
300
850
800
650
525
400
1000 900 800
Calories Burned
700 600 500 400 300 200 100 0 0
1
2
3
4
5
6
7
8
9
10
Miles Run
The number of calories burned seems to increase with the number of miles run.
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The point (5, 600) means that a person who ran 5 miles, burned 600 calories.
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Lesson 15.1 Skills Practice
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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
20
60
5
15
25
30
10
50
Average June Temp. (°F)
75
86
50
102
90
84
81
96
68
y
Latitude vs. Average Temperature
0
10 20 30 40 50 60 70 80 90 Latitude (degrees)
Average Temperature (°F)
180 160 140 120 100 80 60 40 20 0
x
The average temperature in June seems to decrease as the latitude of the location increases.
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The point (60, 50) means that at a latitude of 60° the average temperature in June is 50°F.
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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
0
8
3
2
6
Math Grades (%)
85
90
65
90
100
60
80
95
75
100 90 80
Math Grade (%)
70 60 50 40 30 20 10 0 0
1
2
3
4
5
6
7
8
9
10
Number of Absences
The students’ math grades seem to decrease as their number of absences increase. The point
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(5, 65) means that a student with five absences for the year had a math grade of 65%.
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Lesson 15.1 Skills Practice
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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
1990
2005
1995
2009
2000
1998
2002
1985
1988
2007
Price Per Acre ($)
1300
1650
1200
1800
1500
1350
1700
1100
1250
1750
y
Year vs. Average Price per Acre
Average Price Per Acre ($)
1900 1800 1700 1600 1500 1400 1300 1200 1100 1985
1990
1995 2000 Year
2005
x 2010
As the years increase, the average price of land per acre seems to also increase. The point
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(1995, 1200) means that in the year 1995, the price of land per acre was $1200.
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962 • Chapter 15 Skills Practice
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
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the explanatory variable increases
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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. Sleep and Test Scores
100 90 80
Math Test Score
70 60 50 40 30 20 10 0 0
1
2
3
4
5
6
7
8
9
10
Hours of Sleep
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 © 2011 Carnegie Learning
hours of sleep received increases. The points (5, 100) and (9.5, 70) are potential outliers.
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Name_________________________________________________________ Date__________________________ 2. Suzanne is collecting data for a research paper. She collects the following age and height data for 10 adults. Age vs. Height
y 78
Height (inches)
76 74 72 70 68 66 64 62 60 20
30
40 50 Age (years)
60
x 70
Age is the independent variable and height is the dependent variable. There does not appear to
© 2011 Carnegie Learning
be a linear association, so it is neither positive nor negative and no outliers can be identified.
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3. Scientists studying the Bermuda Triangle measured the ocean’s temperature at various depths. y
Depth vs. Temperature
75
Temperature (°F)
70 65 60 55 50 45 40 35 30
0
500
1000 Depth (feet)
1500
2000
x
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 (2000, 38) is a
© 2011 Carnegie Learning
potential outlier.
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Lesson 15.2 Skills Practice
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Name_________________________________________________________ Date__________________________ 4. A used car dealership collected data about the age of the cars they sold and the price they sold them for. Used Car Prices
20,000 18,000 16,000 14,000
Cost ($)
12,000 10,000 8000 6000 4000 2000 0 0
1
2
3
4
5
6
7
8
9
10
Age of Car
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.
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The point (7, 18,000) is a potential outlier.
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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 10 8 6 4 2 0 56 58 60 62 64 66 68 70 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
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no outliers can be identified.
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Lesson 15.2 Skills Practice
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Name_________________________________________________________ Date__________________________ 6. Hugo has collected data about the unemployment rate in his county over the last several decades. y
Year vs. Unemployment Rate
11.0 10.5
Unemployment Rate (%)
10.0 9.5 9.0 8.5 8.0 7.5 7.0 6.5 6.0 5.5 x 5.0 1970 1975 1980 1985 1990 1995 2000 2005 2010 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
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outliers can be identified.
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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
3.20
Price per Gallon ($)
3.10 3.00 2.90 2.80 2.70 2.60 2.50 2.40 2.30 140
160
180 200 220 240 Gallons Sold (thousands)
260
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
© 2011 Carnegie Learning
of gas sold increases. There do not appear to be any outliers.
970 • Chapter 15 Skills Practice
Lesson 15.2 Skills Practice
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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
4
6 8 10 12 14 16 18 20 22 Advertising Costs (thousands of $)
480 Profit (thousands of $)
460 440 420 400 380 360 340 320 300
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
© 2011 Carnegie Learning
variables. Profit increases as advertising costs increase. The point (20, 410) is a potential outlier.
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972 • Chapter 15 Skills Practice
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
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the table. Number of Practice Balls Thrown
Trial 1 (%)
Trial 2 (%)
Trial 3 (%)
Average Throw Percentage (%)
0
20
20
40
27%
1
40
20
40
33%
2
40
60
40
47%
5
80
80
60
73%
10
80
40
100
73%
15
60
80
100
80%
20
100
80
100
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.
(0, 27); (1, 33); (2, 47); (5, 73); (10, 73); (15, 80); (20, 93)
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Practice Throws and Throw Percentage 100 90
Average Throw Percentage (%)
80 70 60 50 40 30 20 10 0 0
2
4
6
8
10
12
14
16
18
20
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
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 (20, 93) means that after throwing 20 practice throws, the student’s average throw percentage was 93%.
974 • Chapter 15 Skills Practice
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throw percentage.
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 (0, 27) means that after throwing 0 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. Committee Meeting Lengths 100
y
Average Length of Meeting (min.)
90 80 70 60 50 40 30 20 10 x
0 © 2011 Carnegie Learning
0
2
4
6
8
10
12
14
16
18
20
Number of Committee Members
a. Use the data points from the scatter plot to complete the table. Number of Committee Members
3
12
8
20
5
10
5
15
18
Average Meeting Length (min.)
10
25
20
60
15
30
20
35
45
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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. (20, 60); The x-coordinate means that the committee has 20 members. The y-coordinate means that the committee’s meetings last an average of 60 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, 10); You would find the point (3, 10) at the lower left corner of the graph as the values of both coordinates are close to 0. f. Write the ordered pair for the committee with the longest meetings. Explain where you would find the point on the table.
(20, 60); You would look for the largest value along the top row.
members did they have and how long were each of their average meetings? (5, 15) and (5, 20); 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 20 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, 20) and (8, 20); Both committees have an average meeting length of 20 minutes and the first has 5 members and the second has 8 members.
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g. Write the ordered pairs for the committees with the same number of members. How many
