Math Problem Statement

Question 5(Multiple Choice Worth 2 points) (Scatter Plots MC)

A family went on a cross-country road trip for their summer vacation. The following table shows the number of days and the total amount of miles their car had driven.

Number of Days 1 3 7 10 15 Miles Driven 380 984 1,986 2,251 3,623

Which of the following graphs is most appropriate to construct for the data given in the table to observe how the miles change over a certain number of days? Explain. A scatter plot, because it would show how a variable changes over time between each individual data point A scatter plot, because it would show the association, or relationship, between the two variables A line graph, because it would show how a variable changes over time between each individual data point A line graph, because it would show the association, or relationship, between the two variables

Solution

The best option here is:

"A scatter plot, because it would show the association, or relationship, between the two variables."

Explanation:

  • The data provided consists of two variables: number of days and miles driven.
  • A scatter plot is typically used to observe the relationship between two variables. It allows us to see trends, patterns, and potential associations.
  • While line graphs are often used to show continuous changes over time, scatter plots better represent discrete data points and help identify relationships in this case.

Additional Notes:

  • Using a scatter plot, you can visually determine whether the relationship is linear or non-linear.
  • This allows for potential predictions if the trend is consistent.

Would you like me to explain this further or help you visualize this?

Related Questions:

  1. How does a line graph differ from a scatter plot in representing data?
  2. What would a linear trend line indicate if placed on the scatter plot?
  3. How can scatter plots help identify patterns like positive or negative correlations?
  4. What are potential outliers, and how can they be spotted in a scatter plot?
  5. Could a different type of graph (e.g., bar graph) ever be useful for this data?

Tip:

When in doubt about which graph to choose, always ask yourself whether the goal is to observe changes over time or relationships between variables.

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Math Problem Analysis

Mathematical Concepts

Scatter Plots
Data Visualization
Linear Relationships
Graph Interpretation

Formulas

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Theorems

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Suitable Grade Level

Grades 6-9