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The table shows the number of flowers in four bouquets and the total cost of each bouquet.

[tex]\[
\begin{tabular}{|c|c|}
\hline
\text{Number of flowers in the bouquet} & \text{Total cost} \\
\hline
8 & \$12 \\
\hline
12 & \$40 \\
\hline
6 & \$15 \\
\hline
20 & \$20 \\
\hline
\end{tabular}
\][/tex]

What is the correlation coefficient for the data in the table?

A. 0.57
B. -0.28
C. 0.28
D. -0.57

Sagot :

GinnyAnswer
To find the correlation coefficient for the given data, follow these steps:

### Step 1: Organize the Data
Let's rewrite and organize the given data points:

| Number of Flowers | Total Cost ($) |
|-------------------|----------------|
| 8 | 12 |
| 12 | 40 |
| 6 | 15 |
| 20 | 20 |

### Step 2: Understand the Correlation Coefficient
The correlation coefficient measures the strength and direction of the linear relationship between two variables. It is denoted by \( r \) and ranges from -1 to 1:

- \( r = 1 \): Perfect positive linear relationship
- \( r = -1 \): Perfect negative linear relationship
- \( r = 0 \): No linear relationship

### Step 3: Calculate the Correlation Coefficient
For the given number of flowers and total cost, we determine the correlation coefficient to understand their linear relationship better.

### Step 4: Interpret the Result
Following a detailed calculation, the correlation coefficient for the provided data is found to be approximately \( 0.28 \). This indicates a weak positive linear relationship between the number of flowers and the total cost.

Thus, among the given choices, the correct answer is:
0.28
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