To represent the data collected from a family's cross-country road trip, it is essential to choose the most appropriate type of data display. The table provided illustrates the relationship between the number of days and the total miles driven:
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|}
\hline
\text{Number of Days} & 1 & 3 & 7 & 10 & 15 \\
\hline
\text{Miles Driven} & 380 & 984 & 1,986 & 2,251 & 3,623 \\
\hline
\end{tabular}
\][/tex]
For this type of data, which corresponds to measurements taken over time (number of days being the time variable), our goal is to effectively display how the total miles driven changes as the days progress. Reviewing the choices:
1. Histogram: This is used primarily for displaying the distribution of a single variable, typically the frequency of different ranges of values within the data set. This wouldn't be suitable for our data because we are looking at a relationship between two variables rather than the distribution of one.
2. Scatter plot: This graph displays individual data points on a Cartesian plane, often used to examine potential relationships between two variables. While it might show the individual mileage per day, it is not the most effective for displaying trends over time.
3. Line graph: This graph connects data points with lines to show trends over intervals, which is ideal for time-series data. It effectively represents the progression of miles over the days and can clearly display how the total mileage changes as more days pass.
4. Line plot: This term is usually an alternative name for a line graph. Sometimes it may confuse readers who might think it is another variant display.
Given our objective to show trends and changes over an interval (days), the most appropriate data display is a:
Line graph.
A line graph will provide a clear visual representation of the trend in miles driven over the course of the trip, helping to identify patterns, such as periods of more or less travel.
