Scatter Plots and "Best-Fit" Lines


Math in Real Life

NASA's Crawler Transporter is a large vehicle that moves the space shuttle and its launch platform to the launch pad. The crawler uses about 126 gallons of fuel to travel 1 mile.

The table below shows the amount of fuel that is used to travel different numbers of miles. How can you present this information using a graph?


You can represent the information using a scatter plot.  A scatter plot is the graph of a collection of ordered pairs.

Making and Interpreting a Scatter Plot

You can represent and make conclusions about the information above using a scatter plot.

To make a scatter plot, graph the ordered pairs from the table.

(1, 126), (2, 252), (3, 378), (4, 504), (5, 630), (6, 756)

Put Distance on the horizontal axis and Fuel used on the vertical axis.

Answer:  As the distance traveled increases, the amount of fuel used increases. There is exactly one output for each input, so this is a function.


Practice

Make a scatter plot of the data.

1.
 



Interpreting Scatter Plots

Scatter plots show what kind of relationship exists between two sets of data.


Interpreting a Scatter Plot

The table shows the cost y of shipping and handling per item when you buy x items.



a. Make a scatter plot of the data.  Tell whether x and y have a positive relationship, a negative relationship, or no relationship.

Solution

a. In the scatter plot, the y-coordinates decrease as the
x-coordinates increase.

ANSWER: The quantities have a negative relationship.


b. Estimate the cost of shipping and handling per item if you buy eight items.

Solution

b.  To estimate the shipping and handling cost per item to buy eight items, draw a curve that shows the overall pattern of the data, as shown. The curve looks like it will pass through the point (8, 1).

ANSWER The shipping and handling cost per item, if you buy eight items, is about $1.


Practice

2.  Complete the  sentence.

A scatter plot is a graph of a collection of __?__.


3.  Tell whether x and y have a positive relationship, negative relationship, or no relationship.

a.  
 



b.




c.



4.  The table shows the number of cookbooks sold at a bookstore in each of the six years it has been open. Predict the number of cookbooks that will be sold in the ninth year.



Hint!

Step 1  Make a scatter plot.

Step 2  Describe the relationship between the variables.

Step 3  Estimate the number of cookbooks that will be sold in the ninth year by sketching a curve that follows the trend of the data.

Use the information in the table.



5.  Describe the relationship shown in the data.

A. positive
B. negative
C. none
D. not enough information


6.  Predict how many points a player who is 77 inches tall could make.

A. 15
B. 25
C. 65 
D. 85














Answer Key

1. 

2.  ordered pairs

3a.  negative relationship
3b.  no relationship
3c.  positive relationship

4.  about 1700

5.  A

6.  A