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 two quantitative variables: the number of items purchased and the total amount of money spent. A scatter plot allows us to visualize the relationship between these two variables clearly by plotting each customer’s data point on a two-dimensional axis. Conversely, a line graph typically depicts a trend over time or a single variable's progression, which is not suitable for this type of relationship.
### Part B:
To determine the nature of the association between the number of items purchased and the amount spent, we can analyze the data points.
1. **Visual Inspection**: By plotting the data on a scatter plot, we might observe the trend of points. Typically, we would expect that as the number of items increases, the amount spent also increases, indicating a positive association.
2. **Linear vs. Nonlinear**: If the scatter plot shows a roughly straight line sequence where the points cluster closely around a line, the association is linear. If the points curve or show more complexity, it is nonlinear.
3. **Strength of Association**: If the points are tightly packed along the trendline, the association is strong. If the points are spread out and less organized, the association is weak.
Based on the provided data and general understanding of consumer behavior, the association between the number of items purchased and the total amount of money spent appears to be **positive** (as more items generally correlate with more money spent), likely **linear**, and perhaps **moderate to strong**, depending on how closely the data points cluster around the trend line when visualized. This implies that customers who purchase more items tend to spend more money overall in the store.
A scatter plot would be more appropriate for displaying and describing this set of data. This is because the data consists of two quantitative variables: the number of items purchased and the total amount of money spent. A scatter plot allows us to visualize the relationship between these two variables clearly by plotting each customer’s data point on a two-dimensional axis. Conversely, a line graph typically depicts a trend over time or a single variable's progression, which is not suitable for this type of relationship.
### Part B:
To determine the nature of the association between the number of items purchased and the amount spent, we can analyze the data points.
1. **Visual Inspection**: By plotting the data on a scatter plot, we might observe the trend of points. Typically, we would expect that as the number of items increases, the amount spent also increases, indicating a positive association.
2. **Linear vs. Nonlinear**: If the scatter plot shows a roughly straight line sequence where the points cluster closely around a line, the association is linear. If the points curve or show more complexity, it is nonlinear.
3. **Strength of Association**: If the points are tightly packed along the trendline, the association is strong. If the points are spread out and less organized, the association is weak.
Based on the provided data and general understanding of consumer behavior, the association between the number of items purchased and the total amount of money spent appears to be **positive** (as more items generally correlate with more money spent), likely **linear**, and perhaps **moderate to strong**, depending on how closely the data points cluster around the trend line when visualized. This implies that customers who purchase more items tend to spend more money overall in the store.