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Question 2 (Multiple Choice Worth 2 Points)

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.

\begin{tabular}{|c|c|c|c|c|c|}
\hline Number of Days & 1 & 3 & 7 & 10 & 15 \\
\hline Miles Driven & 380 & 984 & 1,986 & 2,251 & 3,623 \\
\hline
\end{tabular}

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

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

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

D. A line graph, because it would show the association, or relationship, between the two variables.



Answer :

GinnyAnswer
To determine the most appropriate graph for the given data, we should carefully consider the nature of the variables and what we want to depict.

We have two variables here:
- The number of days (`1, 3, 7, 10, 15`)
- The miles driven on those days (`380, 984, 1986, 2251, 3623`)

Goal: To find a graphical representation that best shows the relationship between the number of days and the miles driven.

### Analysis of Graph Options

1. Scatter Plot:
- Reason 1: A scatter plot effectively shows how one variable changes with respect to another. Each point on the graph represents a pair (days, miles driven) and we can easily see any patterns or trends.
- Reason 2: Scatter plots are excellent for showing the association or relationship between two variables. In this case, we observe how the miles driven change with the number of days.

2. Line Graph:
- Reason for Usage: Line graphs are often used to show trends over time by connecting data points with lines. This could be helpful to visualize the progression or cumulative addition of miles driven over days.
- Potential Misinterpretation: However, in the context of finding the relation or association between the number of days and the miles driven, connecting these points with lines might suggest continuous data or mislead about values between the recorded days.

### Decision

The best choice for illustrating the relationship between the number of days and the miles driven would be a scatter plot. This is mainly because:

- Clear Visualization: Scatter plots clearly show how one variable (miles driven) is associated with another variable (number of days) without implying intermediate values.
- Detail-Oriented: Each individual data point (days vs. miles) is distinct, and a scatter plot preserves this individuality, making it easier to identify trends and possible outliers.

Answer Explanation:
- Scatter plot shows the association or relationship between the two variables.

Therefore, the most appropriate graph to construct for this data to observe how the miles change over a certain number of days is:
- A scatter plot, because it would show the association, or relationship, between the two variables.

The correct choice is B.

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