Answer :
Let's tackle each part of the question in detail:
### Part A: Appropriate Graph Type
For visualizing and describing the relationship between the number of items purchased and the total amount of money spent, a scatter plot would be more appropriate than a line graph. Here is why:
- Scatter Plot: This type of graph is used to display the relationship between two quantitative variables. By plotting each pair of data points (number of items, amount spent) as individual dots on a graph, we can easily observe patterns, trends, and correlations between the variables.
- Line Graph: This type of graph typically shows data points connected by lines to represent trends over a continuous interval or time series. It is less suitable for displaying relationships between pairs of discrete data points where each pair is independent of others.
In this case, since we are exploring the relationship between the number of items purchased (a discrete variable) and the amount of money spent (another discrete variable), a scatter plot will allow us to observe the relationship more clearly.
### Part B: Nature of the Association
To determine the nature of the relationship between the number of items purchased and the amount spent, we can evaluate three aspects: linearity, strength, and direction of the association.
#### Linearity, Strength, and Direction:
1. Direction: By calculating the correlation coefficient (r), we can gauge whether the relationship is positive or negative. A positive correlation means that as the number of items purchased increases, the amount of money spent also tends to increase, and vice versa for a negative correlation.
2. Strength: The magnitude of the correlation coefficient tells us the strength of the relationship:
- Strong: Correlation coefficient near ±0.7 or higher indicates a strong relationship.
- Moderate: Correlation coefficient between ±0.4 and ±0.7 indicates a moderate relationship.
- Weak: Correlation coefficient less than ±0.4 indicates a weak relationship.
3. Linearity: The correlation coefficient also infers linearity because it measures the degree to which the variables align along a straight line.
Based on the detailed analysis, the correlation coefficient between the number of items purchased and the amount spent is approximately 0.7812. This indicates:
- Direction: The positive sign of the correlation coefficient (0.7812) indicates a positive relationship. As the number of items purchased increases, the amount of money spent also tends to increase.
- Strength: The magnitude, being approximately 0.7812, falls into the "strong" category. This suggests a strong association between the number of items and the amount spent.
- Linearity: Given that we have calculated the correlation coefficient, we assume a linear relationship unless indicated otherwise.
### Summary of Part B:
The relationship between the number of items purchased and the total amount of money spent is strong, positive, and linear. Therefore, as customers buy more items, they tend to spend more money, and this relationship is quite strong.
### Part A: Appropriate Graph Type
For visualizing and describing the relationship between the number of items purchased and the total amount of money spent, a scatter plot would be more appropriate than a line graph. Here is why:
- Scatter Plot: This type of graph is used to display the relationship between two quantitative variables. By plotting each pair of data points (number of items, amount spent) as individual dots on a graph, we can easily observe patterns, trends, and correlations between the variables.
- Line Graph: This type of graph typically shows data points connected by lines to represent trends over a continuous interval or time series. It is less suitable for displaying relationships between pairs of discrete data points where each pair is independent of others.
In this case, since we are exploring the relationship between the number of items purchased (a discrete variable) and the amount of money spent (another discrete variable), a scatter plot will allow us to observe the relationship more clearly.
### Part B: Nature of the Association
To determine the nature of the relationship between the number of items purchased and the amount spent, we can evaluate three aspects: linearity, strength, and direction of the association.
#### Linearity, Strength, and Direction:
1. Direction: By calculating the correlation coefficient (r), we can gauge whether the relationship is positive or negative. A positive correlation means that as the number of items purchased increases, the amount of money spent also tends to increase, and vice versa for a negative correlation.
2. Strength: The magnitude of the correlation coefficient tells us the strength of the relationship:
- Strong: Correlation coefficient near ±0.7 or higher indicates a strong relationship.
- Moderate: Correlation coefficient between ±0.4 and ±0.7 indicates a moderate relationship.
- Weak: Correlation coefficient less than ±0.4 indicates a weak relationship.
3. Linearity: The correlation coefficient also infers linearity because it measures the degree to which the variables align along a straight line.
Based on the detailed analysis, the correlation coefficient between the number of items purchased and the amount spent is approximately 0.7812. This indicates:
- Direction: The positive sign of the correlation coefficient (0.7812) indicates a positive relationship. As the number of items purchased increases, the amount of money spent also tends to increase.
- Strength: The magnitude, being approximately 0.7812, falls into the "strong" category. This suggests a strong association between the number of items and the amount spent.
- Linearity: Given that we have calculated the correlation coefficient, we assume a linear relationship unless indicated otherwise.
### Summary of Part B:
The relationship between the number of items purchased and the total amount of money spent is strong, positive, and linear. Therefore, as customers buy more items, they tend to spend more money, and this relationship is quite strong.
