Here are some key ways to tell the relationship shown in a scatter plot: - Positive relationship: As one variable increases, the other variable also increases. The data points will fall generally above or to the right of the origin. - Negative relationship: As one variable increases, the other decreases. The data points will fall generally below or to the left of the origin. - No relationship: There is no consistent pattern to how the variables change together. The data points will be randomly scattered with no discernible upward or downward trend. Some other clues: - For positive or negative relationships, the data points tend to fall near a straight line. For no relationship, they are more randomly arranged. -

1. Course 3, Lesson 9-1
Solve.
1. The surface area of a rectangular pyramid is 138 square feet.
What is the surface area of a similar solid that has been reduced
by a scale factor of ?
2. The volume of a cone is 34 cubic centimeters. What is the
volume of a similar solid that has been enlarged by a scale
factor of 3?
3. The volume of one cylinder is 600 cubic yards. The volume of a
similar cylinder is 75 cubic yards. What is the scale factor that
relates the two solids?
1
2

2. Course 3, Lesson 9-1
ANSWERS
1. 34.5 ft2
2. 918 cm3
3.
1
2

3. HOW are patterns used
when comparing two quantities?
Statistics and Probability
Course 3, Lesson 9-1

4. Course 3, Lesson 9-1 Common Core State Standards © Copyright 2010. National Governors Association Center for
Best Practices and Council of Chief State School Officers. All rights reserved.
Statistics and Probability
• 8.SP.1
Construct and interpret scatter plots for bivariate measurement data to
investigate patterns of association between two quantities. Describe
patterns such as clustering, outliers, positive or negative association,
linear association, and nonlinear association.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.

5. To
• construct scatter plots,
• interpret data in scatter plots
Course 3, Lesson 9-1
Statistics and Probability

6. • bivariate data
• scatter plot
Course 3, Lesson 9-1
Statistics and Probability

7. 1
Need Another Example?
2
Step-by-Step Example
1. Construct a scatter plot of the number
of viewers who watched new seasons
of a certain television show.
Let the horizontal axis, or x-axis, represent
the number of seasons. Let the vertical
axis, or y-axis, represent the number of
viewers. Then graph the ordered pairs
(season, viewers).

8. Answer
Need Another Example?
Construct a scatter plot
of the distance needed
to stop a car traveling
at each speed.

9. Course 3, Lesson 9-1
Statistics and Probability
Variable Association
Positive Association Negative Association No Association
As x increases, y increases. As x increases, y decreases. No obvious pattern.

10. Course 3, Lesson 9-1
Statistics and Probability
Linear Association Linear Nonlinear
The data points lie close to a
line.
The data points lie in the
shape of a curve.

11. 1
Need Another Example?
2
3
4
Step-by-Step Example
2. Interpret the scatter plot
of the data for the amount
of memory in an MP3
player and the cost based
on the shape of the
distribution.
Consider the different associations
and patterns.
Variable Association As the amount of memory increases, the
cost increases. Therefore, the scatter plot
shows a positive association.
Linear Association The data appear to lie close to a line,
so the association is linear.
Other Patterns There appears to be a cluster of data.
One to two gigabytes of memory costs
between $30 and $75. There does not
appear to be an outlier.

12. Answer
Need Another Example?
Interpret the scatter plot of the data for
cups of hot chocolate sold and the
outside temperature based on the
shape of the distribution.
As temperature increases, the number of cups
sold decreases. So, the scatter plot shows a
negative association. The data appear to lie
close to a line, so the association is linear.
There are no clusters or outliers.

13. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
3. The table shows public school enrollment from 1999-2010.
Construct a scatter plot of the data. Let the
horizontal axis represent the year since 1999 and
the vertical axis represent the number of students.
Consider the different associations and patterns.
Variable Association As the years increase, the number of students increases.
Therefore, the scatter plot shows a positive association.
Construct and interpret a scatter plot of the
data. If an association exists, make a conjecture
about the number of students that will be
enrolled in public schools in the year 2015.
To make a conjecture about the number of students that will be enrolled in public
schools in the year 2015, follow the pattern until the x-value is 16. Then find the
corresponding y-value.
Linear Association The data appear to lie close to a line, so the association is
linear.
Other Patterns There are no clusters or outliers.
So, there will be about 51 million students enrolled in
public schools in 2015.

14. Answer
Need Another Example?
The table shows the average extra fuel used by drivers in one city due to
travel delays in congested areas. Construct and interpret a scatter plot of
the data. If an association exists, make a conjecture about the excess
fuel that will be used by an average driver in 2020.
As the years increase, the excess fuel
increases. So, the scatter plot shows a
positive association. The data appear to
lie close to a line, so the association is
linear. There are no clusters or outliers;
Sample answer: about 42 gallons.

15. How did what you learned
today help you answer the
How are patterns used
when comparing two quantities?
Course 3, Lesson 9-1
GeometryStatistics and Probability

16. How did what you learned
today help you answer the
How are patterns used
when comparing two quantities?
Course 3, Lesson 9-1
GeometryStatistics and Probability
Sample answers:
• You can graph bivariate data on a coordinate plane to
determine if there are patterns between the data.
• In a scatter plot, patterns in the data can determine
whether the association is positive, negative , or that
there is no association between bivariate data.
• The association can also be linear or nonlinear.

17. How can you tell whether a
scatter plot shows a positive,
negative, or no relationship?
Course 3, Lesson 9-1
Ratios and Proportional RelationshipsFunctionsStatistics and Probability