Question
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 3 4 6 9 12
Miles Driven 942 1,027 1,543 1,965 2,704
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 line graph, 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 scatter plot, because it would show the association, or relationship, between the two variables
A scatter plot, because it would show how a variable changes over time between each individual data point
Number of Days 3 4 6 9 12
Miles Driven 942 1,027 1,543 1,965 2,704
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 line graph, 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 scatter plot, because it would show the association, or relationship, between the two variables
A scatter plot, because it would show how a variable changes over time between each individual data point
Answers
GPT-4o mini
To determine the most appropriate graph for displaying the relationship between the number of days and the miles driven for the family's road trip, we should consider the characteristics of the data and the purpose of the graph.
1. **Line Graph**: This type of graph is useful for showing trends over time or a continuous relationship between two variables. If we expect the miles driven to vary continuously as the number of days increases, a line graph could effectively depict that trend.
2. **Scatter Plot**: This graph is ideal for showing the relationship between two variables by plotting individual data points. While it can help identify correlation and the overall pattern, it may not clearly illustrate trends over longer intervals like a line graph does.
Given the options provided:
- "A line graph, because it would show the association, or relationship, between the two variables" emphasizes the relationship but is less specific about observing changes.
- "A line graph, because it would show how a variable changes over time between each individual data point" correctly captures the essence of demonstrating the change over time.
- "A scatter plot, because it would show the association, or relationship, between the two variables" points to identifying correlation but may not adequately express how miles driven changes over days.
- "A scatter plot, because it would show how a variable changes over time between each individual data point" is incorrect because scatter plots do not typically demonstrate changes over intervals for continuous data in the same way line graphs do.
Based on these considerations, the best answer is:
**A line graph, because it would show how a variable changes over time between each individual data point.**
This choice illustrates the trend of miles driven over the increasing number of days effectively.
1. **Line Graph**: This type of graph is useful for showing trends over time or a continuous relationship between two variables. If we expect the miles driven to vary continuously as the number of days increases, a line graph could effectively depict that trend.
2. **Scatter Plot**: This graph is ideal for showing the relationship between two variables by plotting individual data points. While it can help identify correlation and the overall pattern, it may not clearly illustrate trends over longer intervals like a line graph does.
Given the options provided:
- "A line graph, because it would show the association, or relationship, between the two variables" emphasizes the relationship but is less specific about observing changes.
- "A line graph, because it would show how a variable changes over time between each individual data point" correctly captures the essence of demonstrating the change over time.
- "A scatter plot, because it would show the association, or relationship, between the two variables" points to identifying correlation but may not adequately express how miles driven changes over days.
- "A scatter plot, because it would show how a variable changes over time between each individual data point" is incorrect because scatter plots do not typically demonstrate changes over intervals for continuous data in the same way line graphs do.
Based on these considerations, the best answer is:
**A line graph, because it would show how a variable changes over time between each individual data point.**
This choice illustrates the trend of miles driven over the increasing number of days effectively.