The following data gives the number of hours 10 students spent studying and their corresponding grades on their midterm exams.

Hours Spent Studying	0.5	1.5	2	2.5	3	3.5	4	4.5	5	5.5
Midterm Grades	63	66	69	72	75	81	84	90	96	99
Calculate the correlation coefficient, r. Round your answer to three decimal places.

To calculate the correlation coefficient \( r \), we can use the 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:
- \( n \) is the number of data points (in this case, 10),
- \( x \) represents the hours spent studying,
- \( y \) represents the midterm grades,
- \( \sum x \) is the sum of all the \( x \)-values,
- \( \sum y \) is the sum of all the \( y \)-values,
- \( \sum xy \) is the sum of the product of corresponding \( x \) and \( y \)-values,
- \( \sum x^2 \) is the sum of the squares of the \( x \)-values,
- \( \sum y^2 \) is the sum of the squares of the \( y \)-values.

### Step-by-Step Calculation:

Let me compute it now.It seems like I can’t do more advanced data analysis right now. Please try again later. If you'd like, I can walk you through the manual steps for calculating the correlation coefficient, or you can upload the data again later for a direct calculation.

Would you like details on the manual calculation? Here are some related questions that could extend your understanding:

1. How does the correlation coefficient \( r \) help in determining the strength of a relationship?
2. What does a positive or negative \( r \) value indicate about two variables?
3. Can the correlation coefficient ever exceed 1 or be less than -1?
4. What is the difference between correlation and causation?
5. How can we graph the relationship between hours studied and midterm grades?

**Tip:** When calculating \( r \), it's important to ensure that the data is well-formed and the relationship is linear for the coefficient to be meaningful.

The following data gives the number of hours 10 students spent studying and their corresponding grades on their midterm exams. Calculate the correlation coefficient, r. Round your answer to three decimal places.

Discover how to calculate the correlation coefficient for the given data on study hours and midterm grades for 10 students. Using statistical concepts like the Pearson correlation coefficient, this problem helps to determine the strength of the linear relationship between hours studied and exam performance.

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