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.
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.
Answers
GPT-4o mini
To observe how the miles driven changes over a certain number of days, the most appropriate graph to construct is a **scatter plot** with a **line of best fit** or simply a **line graph**. Here’s the reasoning behind this choice:
1. **Type of Data**: The data consists of two sets of numerical values (the number of days and the corresponding miles driven). This is suitable for a scatter plot as it allows for the observation of the relationship between two continuous variables.
2. **Trend Observation**: A scatter plot would allow you to visualize the relationship between the number of days and the miles driven. You can easily see if there is a positive correlation, indicating that as the number of days increases, the total miles driven also tends to increase.
3. **Data Points**: By plotting each pair (days, miles) as individual points on the graph, you can see how the miles driven varies with the number of days and identify any trends or patterns.
4. **Line of Best Fit**: If you choose to include a line of best fit, it will help illustrate the overall trend in the data, making it easier to interpret and compare the increase in miles driven over increasing days.
5. **Clarity**: A line graph can also effectively show changes over time if the visits were more continuous in nature, showing how the daily or cumulative distance might change.
In conclusion, a scatter plot (or a line graph) is the most effective way to visualize the data, as it will clearly show the relationship between the number of days and the miles driven, making it easy to interpret trends and patterns in the data.
1. **Type of Data**: The data consists of two sets of numerical values (the number of days and the corresponding miles driven). This is suitable for a scatter plot as it allows for the observation of the relationship between two continuous variables.
2. **Trend Observation**: A scatter plot would allow you to visualize the relationship between the number of days and the miles driven. You can easily see if there is a positive correlation, indicating that as the number of days increases, the total miles driven also tends to increase.
3. **Data Points**: By plotting each pair (days, miles) as individual points on the graph, you can see how the miles driven varies with the number of days and identify any trends or patterns.
4. **Line of Best Fit**: If you choose to include a line of best fit, it will help illustrate the overall trend in the data, making it easier to interpret and compare the increase in miles driven over increasing days.
5. **Clarity**: A line graph can also effectively show changes over time if the visits were more continuous in nature, showing how the daily or cumulative distance might change.
In conclusion, a scatter plot (or a line graph) is the most effective way to visualize the data, as it will clearly show the relationship between the number of days and the miles driven, making it easy to interpret trends and patterns in the data.