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.

Question

Number of Items 1 5 3 9 7 4 2 1 6 10 5 8
Amount Spent (in dollars) 220 160 168 114 95 147 178 184 143 78 109 94

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)

Answer 1

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 bought and the total amount spent. Each point on the scatter plot will represent an individual customer's spending behavior, allowing for visual analysis of patterns and associations between the two variables. A line graph, on the other hand, is generally used to show trends over time or continuous data, which does not suit the nature of this dataset.

Part B:

To determine the relationship between the number of items purchased and the total amount of money spent, we need to consider the pattern in the data. Based on a visual inspection of a scatter plot created from the data:

1. Association Type: The association appears to be nonlinear when looking at how the spending does not consistently increase or decrease with the number of items purchased.

2. Strength of Association: The data points seem to be somewhat scattered, which indicates a weak correlation. While there may be some upward trend (as mostly more items tend to correspond with more spending), there are also several instances where customers purchased a similar number of items but spent significantly different amounts. This scattered nature indicates that while there is some relationship, it is not very strong.

3. Direction of Association: The relationship tends to be positive for lower to moderate numbers of items purchased, meaning that as the number of items increases, the amount spent also tends to increase. However, due to the variability in amounts spent for some similar numbers of items purchased, it highlights the individual variations in spending that affect this overall trend.

In summary, the relationship is characterized as nonlinear, weak, and generally positive, indicating that while there is some tendency for spending to increase with the number of items purchased, it is influenced by other factors that contribute to the variability in spending amounts.