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To solve the problem and find the **correlation coefficient** for the given data, we need to calculate the correlation between the **Month** (1 to 12) and the corresponding **Temperature (°F)**.

The correlation coefficient (\(r\)) can be calculated using the Pearson formula:

\[
r = \frac{n \sum (XY) - \sum X \sum Y}{\sqrt{(n \sum X^2 - (\sum X)^2)(n \sum Y^2 - (\sum Y)^2)}}
\]

Where:
- \(X\) is the month,
- \(Y\) is the temperature,
- \(n\) is the number of data points (which is 12 in this case).

I'll calculate the correlation coefficient for the data using the table.The **correlation coefficient** between the month and the temperature in Austin, Texas, is approximately **0.0416**. 

This value indicates a very weak positive linear association between the month and the temperature. In other words, the month of the year does not have a strong influence on the temperature changes according to this data set.

Would you like further details on how this is calculated or interpreted?

Here are five questions to consider:
1. How does a positive correlation coefficient affect the relationship between two variables?
2. What are the potential limitations of using correlation to assess relationships?
3. Can the correlation coefficient indicate causality between the month and temperature?
4. How does a correlation coefficient close to zero influence predictions in real-world scenarios?
5. What would a negative correlation coefficient suggest about the month and temperature?

**Tip:** Always remember that correlation measures the strength of a linear relationship, but does not necessarily imply causation!

The table shows the monthly high temperature for Austin, Texas, in degrees Fahrenheit over a 12-month period. What does the correlation coefficient for the data indicate about the strength of the linear association between the month and the temperature in Austin?

Analyze the correlation coefficient between the month and the high temperature data in Austin, Texas, over a 12-month period. Understand the strength of the linear association and what it indicates. Suitable for students in Grades 9-12.

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