To find the correlation coefficient for the data in the table, follow these steps:
### Step 1: Understand the Data
We have two sets of values:
1. Number of flowers in the bouquet: [tex]\([8, 12, 6, 20]\)[/tex]
2. Total cost of each bouquet: [tex]\([12, 40, 15, 20]\)[/tex]
### Step 2: Interpret Correlation Coefficient
The correlation coefficient measures the degree to which two variables are linearly related. It ranges from -1 to 1, where:
- [tex]\(1\)[/tex] indicates a perfect positive linear relationship,
- [tex]\(-1\)[/tex] indicates a perfect negative linear relationship,
- [tex]\(0\)[/tex] indicates no linear relationship.
### Step 3: Calculate the Correlation Coefficient
Based on the data provided and the calculations, the result for the correlation coefficient between the number of flowers and the total cost is approximately [tex]\(0.28\)[/tex].
This means there is a weak positive linear relationship between the number of flowers in the bouquet and the total cost.
### Step 4: Select the Correct Answer
Given the choices:
- [tex]\(-0.57\)[/tex]
- [tex]\(-0.28\)[/tex]
- [tex]\(0.28\)[/tex]
- [tex]\(0.57\)[/tex]
The correct answer is [tex]\(0.28\)[/tex].
This value shows that as the number of flowers increases, the total cost tends to increase to some extent, but the relationship is not very strong.
