Question
A manager at a retail store was interested in the spending habits of customers during the holiday season. The manager surveyed a random group of customers and recorded the number of items that they bought, and the total amount of money they spent at the store. The table displays the information collected on the customers.
Number of Items 1 5 3 8 7 4 3 1 6 8 4 8
Amount Spent (in dollars) 22 92 57 470 204 102 81 85 152 780 52 455
Part A: Would a scatter plot or line graph be more appropriate for displaying and describing this set of data? Explain. (2 points)
Part B: Determine whether the association is linear or nonlinear, strong or weak, and positive or negative and use it to describe the relationship between the number of items purchased and the total amount of money spent. (2 points)
Number of Items 1 5 3 8 7 4 3 1 6 8 4 8
Amount Spent (in dollars) 22 92 57 470 204 102 81 85 152 780 52 455
Part A: Would a scatter plot or line graph be more appropriate for displaying and describing this set of data? Explain. (2 points)
Part B: Determine whether the association is linear or nonlinear, strong or weak, and positive or negative and use it to describe the relationship between the number of items purchased and the total amount of money spent. (2 points)
Answers
GPT-4o mini
### Part A:
A scatter plot would be more appropriate for displaying and describing this set of data. This is because the data consists of pairs of numerical values (the number of items bought and the amount spent), which can be plotted as individual points on a scatter plot. A scatter plot allows us to visualize the relationship between these two quantitative variables, whereas a line graph is better suited for displaying trends over time or continuous data. Since the data does not represent a time series or continuous function, a scatter plot is the best choice.
### Part B:
To determine the nature of the association between the number of items purchased and the total amount of money spent, we can analyze the relationship based on the provided data points:
- From the data, we generally observe that as the number of items purchased increases, the amount spent tends to increase as well.
- This suggests a **positive** association.
- To evaluate whether the relationship is **linear or nonlinear**, we can consider the nature of the increase. Although spending does increase with the number of items, the amount by which it increases varies significantly—specifically, large purchases (e.g., buying 8 items) result in a disproportionately higher amount spent compared to smaller purchases. This variability suggests that the relationship is likely **nonlinear** rather than perfectly linear.
- With respect to **strength**, the association appears to be relatively **strong** because most of the data points cluster in a way that indicates a clear upward trend, albeit non-linearly.
In conclusion, the relationship between the number of items purchased and the total amount of money spent is **positive**, **nonlinear**, and **strong**, indicating that as a customer buys more items, they typically spend more money in the store, though the rate of spending increase varies.
A scatter plot would be more appropriate for displaying and describing this set of data. This is because the data consists of pairs of numerical values (the number of items bought and the amount spent), which can be plotted as individual points on a scatter plot. A scatter plot allows us to visualize the relationship between these two quantitative variables, whereas a line graph is better suited for displaying trends over time or continuous data. Since the data does not represent a time series or continuous function, a scatter plot is the best choice.
### Part B:
To determine the nature of the association between the number of items purchased and the total amount of money spent, we can analyze the relationship based on the provided data points:
- From the data, we generally observe that as the number of items purchased increases, the amount spent tends to increase as well.
- This suggests a **positive** association.
- To evaluate whether the relationship is **linear or nonlinear**, we can consider the nature of the increase. Although spending does increase with the number of items, the amount by which it increases varies significantly—specifically, large purchases (e.g., buying 8 items) result in a disproportionately higher amount spent compared to smaller purchases. This variability suggests that the relationship is likely **nonlinear** rather than perfectly linear.
- With respect to **strength**, the association appears to be relatively **strong** because most of the data points cluster in a way that indicates a clear upward trend, albeit non-linearly.
In conclusion, the relationship between the number of items purchased and the total amount of money spent is **positive**, **nonlinear**, and **strong**, indicating that as a customer buys more items, they typically spend more money in the store, though the rate of spending increase varies.