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?
Scatterplot is the appropriate graphical display to identify relationships between two variables.
A scatterplot visually represents the relationship between two quantitative variables, allowing the restaurant owner to observe patterns, trends, or correlations between daily revenue and percent change in the stock market index fund.
A box plot is primarily used to display the distribution of a single quantitative variable, highlighting its median, quartiles, and potential outliers. It does not effectively illustrate relationships between two different variables, which is essential for the restaurant owner’s analysis of revenue versus stock market changes.
As stated, a scatterplot is the best choice for exploring the relationship between the daily revenue and the percent change in a stock market index fund. Each point on the scatterplot represents a day, with the x-axis denoting one variable and the y-axis the other, making it easy to identify any correlation or trend.
A stem-and-leaf plot provides a way to display quantitative data while preserving the original data values. However, it is mainly used for summarizing a single variable rather than examining the relationship between two variables, thus making it unsuitable for the restaurant owner's needs.
A histogram is utilized to display the frequency distribution of a single quantitative variable. While useful for understanding the distribution of daily revenue or percent changes separately, it does not reveal any potential correlation between the two variables, which is the owner’s aim.
To analyze the relationship between daily revenue and stock market index changes effectively, a scatterplot is the most suitable graphical representation. It allows the restaurant owner to visualize correlations and trends, facilitating a clearer understanding of how these two variables interact over time. Other options like box plots, stem-and-leaf plots, and histograms focus on single-variable analysis and fail to meet the specific needs of this inquiry.
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