# Scatter Plots

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Examples, solutions, and videos to help Grade 8 students learn how to use scatter plots to investigate relationships and understand the distinction between a statistical relationship and a cause-and-effect relationship.

### New York State Common Core Math Grade 8, Module 6, Lesson 6

Lesson 6 Student Outcomes

• Students construct scatter plots.
• Students use scatter plots to investigate relationships.
• Students understand the distinction between a statistical relationship and a cause-and-effect relationship.

Lesson 6 Summary

• A scatter plot is a graph of numerical data on two variables.
• A pattern in a scatter plot suggests that there may be a relationship between the two variables used to construct the scatter plot.
• If two variables tend to vary together in a predictable way, we can say that there is a statistical relationship between the two variables.
• A statistical relationship between two variables does not imply that a change in one variable causes a change in the other variable (a cause-and-effect relationship).

Lesson 6 Classwork

Example 1
A bivariate data set consists of observations on two variables. For example, you might collect data on 13 different car models. Each observation in the data set would consist of an (x, y) pair.
x = weight (in pounds, rounded to the nearest 50 pounds)
and
y = fuel efficiency (in miles per gallon, mpg.)
The table below shows the weight and fuel efficiency for 13 car models with automatic transmissions manufactured in 2009 by Chevrolet.

Exercises 1–3
1. In the table above, the observation corresponding to model 1 is (3200, 23). What is the fuel efficiency of this car? What is the weight of this car?
2. Add the points corresponding to the other 12 observations to the scatter plot.
3. Do you notice a pattern in the scatter plot? What does this imply about the relationship between weight (x) and fuel efficiency (y)?

Exercises 4–8
Is there a relationship between price and the quality of athletic shoes? The data in the table below are from the Consumer Reports website.
x = price (in dollars)
and
y = Consumer Reports quality rating
The quality rating is on a scale of 0 to 100, with 100 being the highest quality.

4. One observation in the data set is (110, 57). What does this ordered pair represent in terms of cost and quality?

5. To construct a scatter plot of these data, you need to start by thinking about appropriate scales for the axes of the scatter plot. The prices in the data set range from \$30 to \$110, so one reasonable choice for the scale of the x-axis would range from \$20 to \$120, as shown below. What would be a reasonable choice for a scale for the y-axis?

6. Add a scale to the -axis. Then, use these axes to construct a scatter plot of the data.

7. Do you see any pattern in the scatter plot indicating that there is a relationship between price and quality rating for athletic shoes?

8. Some people think that if shoes have a high price, they must be of high quality. How would you respond?

Example 2
A pattern in a scatter plot indicates that the values of one variable tend to vary in a predictable way as the values of the other variable change. This is called a statistical relationship. In the fuel efficiency and car weight example, fuel efficiency tended to decrease as car weight increased.
This is useful information, but be careful not to jump to the conclusion that increasing the weight of a car causes the fuel efficiency to go down. There may be some other explanation for this. For example, heavier cars may also have bigger engines, and bigger engines may be less efficient. You cannot conclude that changes to one variable cause changes in the other variable just because there is a statistical relationship in a scatter plot.

Exercises 9–10
9. Data were collected on
x = shoe size
and
y = score on a reading ability test
for 30 elementary school students. The scatter plot of these data is shown below. Does there appear to be a statistical relationship between shoe size and score on the reading test?

10. Explain why it is not reasonable to conclude that having big feet causes a high reading score. Can you think of a different explanation for why you might see a pattern like this?

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