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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. (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 spe

1 answer

Part A:

A scatter plot would be more appropriate for displaying and describing this set of data. This is because scatter plots are designed to show the relationship between two quantitative variables—in this case, the number of items purchased and the total amount spent. A scatter plot allows for visualizing the distribution of data points and any potential correlations between the two variables. In contrast, a line graph is typically used to display trends over time or for continuous data where the values are sequential. Since the data in this scenario does not represent a continuous time sequence but rather two sets of numerical values, a scatter plot is the most suitable choice.

Part B:

To determine whether the association between the number of items purchased and the total amount of money spent is linear or nonlinear, strong or weak, and positive or negative, we can analyze the data visually through a scatter plot or mathematically using correlation.

Visual Analysis: Plotting the data points on a scatter plot would allow us to see the trend. Generally, one would expect that as the number of items purchased increases, the total amount spent would also increase, suggesting a positive correlation.

Correlation Analysis: If we calculate the correlation coefficient (using statistical software or a calculator), we might find a value close to +1, indicating a strong positive linear relationship. For this example, we can qualitatively analyze the data without doing calculations:

  • Linear or Nonlinear: From the presented data, it seems that as the number of items increases, the spending also increases, suggesting a linear or roughly linear relationship.
  • Strong or Weak: If the points form a tight cluster around a line when plotted, the correlation would be considered strong. If they are widely dispersed, it would indicate a weak correlation.
  • Positive or Negative: Given the nature of the data (people tend to spend more as they purchase more items), we can conclude that the relationship is positive.

In summary:

  • The association appears to be linear.
  • The correlation is likely strong based on the expected clustering of points.
  • The relationship is positive, indicating that customers tend to spend more money as they purchase a greater number of items.