Question
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 2 5 6 8 12
Miles Driven 425 967 1,253 1,253 2,648
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 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
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
Number of Days 2 5 6 8 12
Miles Driven 425 967 1,253 1,253 2,648
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 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
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
Answers
GPT-4o mini
The most appropriate choice for the data given in the table is:
**A line graph, because it would show how a variable changes over time between each individual data point.**
Here’s why this option is the best choice:
1. **Nature of the Data**: The data represents miles driven over a specific number of days, which can be considered sequential time intervals. A line graph is effective for showing changes in a variable over time.
2. **Continuous Relationship**: A line graph can show the trend and progression of mileage as the number of days increases. This clear visual representation helps in understanding how the miles driven change as the duration of the trip increases.
3. **Data Points Connection**: While a scatter plot shows individual data points and their relationship, a line graph connects these points, emphasizing the continuity and overall trend, which is more relevant when analyzing how miles driven evolve over days.
In summary, a line graph effectively conveys the relationship and changes in mileage over time, thus making it the ideal representation for this particular dataset.
**A line graph, because it would show how a variable changes over time between each individual data point.**
Here’s why this option is the best choice:
1. **Nature of the Data**: The data represents miles driven over a specific number of days, which can be considered sequential time intervals. A line graph is effective for showing changes in a variable over time.
2. **Continuous Relationship**: A line graph can show the trend and progression of mileage as the number of days increases. This clear visual representation helps in understanding how the miles driven change as the duration of the trip increases.
3. **Data Points Connection**: While a scatter plot shows individual data points and their relationship, a line graph connects these points, emphasizing the continuity and overall trend, which is more relevant when analyzing how miles driven evolve over days.
In summary, a line graph effectively conveys the relationship and changes in mileage over time, thus making it the ideal representation for this particular dataset.