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.

Question

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

Answer 1

The most appropriate choice for the given data is:

A line graph, because it would show how a variable changes over time between each individual data point.

Explanation:

1. Nature of the Data: The data consists of two variables: the number of days (independent variable) and the total miles driven (dependent variable). Since the number of days is a continuous range, a line graph is effective in illustrating the trends over time.

2. Time Series Data: The number of days represents time progression, and using a line graph allows us to visually represent changes over this continuous variable. It connects the points, making it easier to see how the miles driven changes as the number of days increases.

3. Direction of Relationship: Using a line graph emphasizes the trend and direction of the relationship between the two variables over time, which can be informative for a cross-country trip's mileage accumulation.

While a scatter plot could show the relationship as well, it would not emphasize the change over time in the way that a line graph would, especially when interpreting the cumulative nature of driving over increasing days.