40. For each of 100 days, a restaurant owner recorded the total revenue for the day along with the percent change in a stock market index fund. The owner would like to create a visual display to better identify if a relationship exists between the two variables. Which type of graphical display should be used?
Answer: B
Scatterplot is the appropriate graphical display for identifying relationships between two variables.
A scatterplot will effectively illustrate the relationship between the restaurant's revenue and the percent change in the stock market index fund over the 100 days.
A) Box plot
A box plot is designed to summarize the distribution of a dataset, particularly highlighting the median, quartiles, and potential outliers. While it provides insights into the spread and central tendency of a single variable, it does not effectively display relationships between two different variables, making it unsuitable for this analysis.
B) Scatterplot
A scatterplot is the ideal choice for this scenario as it allows for the visualization of two quantitative variables, enabling the restaurant owner to observe potential correlations or trends between daily revenue and changes in the stock market index. Each point on the scatterplot represents a day's revenue against the corresponding percent change, facilitating the identification of any relationship.
C) Stem-and-leaf plot
A stem-and-leaf plot is primarily used to display the distribution of a single quantitative variable while retaining the original data values. Although it can show the shape of a dataset, it does not provide a means to compare two variables simultaneously, making it inadequate for assessing the relationship in question.
D) Histogram
A histogram is useful for illustrating the distribution of a single variable, showing frequency counts of data within specified intervals. However, it does not allow for the evaluation of relationships between two different variables, such as revenue and stock market changes, thus failing to meet the requirements of the analysis.
Conclusion
The scatterplot is definitively the correct choice as it provides a clear visual representation of the relationship between two quantitative variables, which is essential for the restaurant owner's analysis. All other options either focus on summarizing one variable or fail to show the relationship between the two variables effectively. Therefore, the scatterplot is the most appropriate tool for this purpose.