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.
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.
Answer (2)
A scatter plot is the best choice for visualizing the data, as it shows the relationship between two quantitative variables. The association between the number of items purchased and the amount spent is positive and moderately strong, indicating that spending tends to increase with the number of items bought.
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A scatter plot is more appropriate for visualizing the relationship between the number of items purchased and the amount spent.
The association between the number of items and the amount spent is positive.
The association is moderately strong, with a correlation coefficient of approximately 0.79.
As the number of items purchased increases, the total amount spent tends to increase, indicating a positive relationship. Positive and Moderately Strong
Explanation
Understanding the Problem We are given a dataset of customers' spending habits during the holiday season, including the number of items purchased and the total amount spent. Part A asks us to choose the more appropriate graph type (scatter plot or line graph) for displaying this data, and Part B requires us to describe the association between the two variables.
Choosing the Right Graph For Part A, a scatter plot is more appropriate for displaying the relationship between two quantitative variables (number of items and amount spent). Each point on the scatter plot represents a customer, with the x-coordinate being the number of items purchased and the y-coordinate being the amount spent. A line graph is typically used to show how a single variable changes over time.
Analyzing the Association For Part B, we need to determine the nature of the association. To do this, we can analyze the data to see if there's a trend. The correlation coefficient between the number of items and the amount spent is approximately 0.79. This indicates a positive association.
Describing the Relationship Since the correlation coefficient is 0.79, the association is considered relatively strong. As the number of items purchased increases, the total amount of money spent also tends to increase. The relationship appears to be somewhat linear, although there might be some curvature or outliers.
Final Answer In summary: Part A: A scatter plot is more appropriate because it displays the relationship between two quantitative variables. Part B: The association is positive and moderately strong, suggesting that as the number of items purchased increases, the total amount spent also tends to increase.
Examples
Understanding the relationship between the number of items purchased and the amount spent can help a retail store manager make informed decisions about inventory, marketing strategies, and staffing levels. For example, if the manager knows that customers who buy more items tend to spend significantly more money, they might create promotions that encourage customers to add more items to their carts. This type of analysis can also help in predicting sales trends and optimizing resource allocation during peak seasons.
