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 9 7 4 3 1 6 10 4 8
Amount Spent (in dollars) 38 82 143 160 114 102 81 85 95 220 52 140
Part A: Would a scatter plot or line graph be more appropriate for displaying and describing this set of data? Explain.
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.
Number of Items 1 5 3 9 7 4 3 1 6 10 4 8
Amount Spent (in dollars) 38 82 143 160 114 102 81 85 95 220 52 140
Part A: Would a scatter plot or line graph be more appropriate for displaying and describing this set of data? Explain.
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.
Answers
GPT-4o mini
### Part A:
A **scatter plot** would be more appropriate for displaying and describing this set of data. This is because a scatter plot is specifically designed to show the relationship between two quantitative variables—in this case, the number of items purchased and the total amount of money spent. A line graph is typically used to show trends over time or ordered categories, and since the data points do not represent a continuous variable over time or an ordered category, a scatter plot is the better choice for visualizing the potential relationship between these two variables.
### Part B:
To determine the nature of the association between the number of items purchased and the total amount spent, we would typically visualize the data points on a scatter plot. However, based on the data provided, we can analyze the relationship:
1. **Linear or Nonlinear**:
- Given that the amount spent generally increases as the number of items purchased increases, we can hypothesize that the relationship could be linear. However, to confirm this, we would generally look to see if the points align closely in a straight pattern or if they appear to curve or follow a different pattern.
2. **Strong or Weak**:
- After plotting or analyzing the data, if we find that the points cluster closely around a line (indicating a consistent relationship), we would conclude the relationship is **strong**. If they are more scattered and do not clearly form a pattern, the relationship may be deemed **weak**.
3. **Positive or Negative**:
- Because the amount spent tends to increase with the number of items purchased, we can conclude that the association is **positive**.
### Conclusion:
Based on this reasoning, we would describe the relationship as:
- The association between the number of items purchased and the total amount of money spent is likely **linear** and **strong**, and it is a **positive** relationship, indicating that as customers buy more items, they generally spend more money at the store. For a more accurate analysis, performing a correlation coefficient calculation or a regression analysis would provide more definitive insights.
A **scatter plot** would be more appropriate for displaying and describing this set of data. This is because a scatter plot is specifically designed to show the relationship between two quantitative variables—in this case, the number of items purchased and the total amount of money spent. A line graph is typically used to show trends over time or ordered categories, and since the data points do not represent a continuous variable over time or an ordered category, a scatter plot is the better choice for visualizing the potential relationship between these two variables.
### Part B:
To determine the nature of the association between the number of items purchased and the total amount spent, we would typically visualize the data points on a scatter plot. However, based on the data provided, we can analyze the relationship:
1. **Linear or Nonlinear**:
- Given that the amount spent generally increases as the number of items purchased increases, we can hypothesize that the relationship could be linear. However, to confirm this, we would generally look to see if the points align closely in a straight pattern or if they appear to curve or follow a different pattern.
2. **Strong or Weak**:
- After plotting or analyzing the data, if we find that the points cluster closely around a line (indicating a consistent relationship), we would conclude the relationship is **strong**. If they are more scattered and do not clearly form a pattern, the relationship may be deemed **weak**.
3. **Positive or Negative**:
- Because the amount spent tends to increase with the number of items purchased, we can conclude that the association is **positive**.
### Conclusion:
Based on this reasoning, we would describe the relationship as:
- The association between the number of items purchased and the total amount of money spent is likely **linear** and **strong**, and it is a **positive** relationship, indicating that as customers buy more items, they generally spend more money at the store. For a more accurate analysis, performing a correlation coefficient calculation or a regression analysis would provide more definitive insights.