https://file.aiquickdraw.com/mathbot/file/1727915929895z6jjfkbm.jpg

To find the correlation coefficient (often denoted as **r**) between the number of absences and math grades, we use Pearson's correlation 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:
- \( x \) represents the number of absences,
- \( y \) represents the math grades,
- \( n \) is the number of data points.

Let's extract the data from the table:

\[
\text{Number of Absences } (x) = [3, 2, 5, 1, 0, 8, 3, 2, 6]
\]
\[
\text{Math Grades } (y) = [85, 90, 65, 90, 100, 60, 80, 95, 75]
\]

Now, I will calculate the correlation coefficient using this data.

Let me compute this for you.The correlation coefficient between the number of absences and math grades is approximately **-0.93**, rounded to the nearest hundredth. This indicates a strong negative correlation, meaning that as the number of absences increases, math grades tend to decrease significantly.

Would you like any more details on the calculation or have any further questions?

Here are 5 related questions you might find interesting:
1. What is the interpretation of a correlation coefficient close to -1?
2. How would this correlation be affected if the outliers were removed?
3. Can you think of other factors that might influence math grades aside from absences?
4. What is the difference between correlation and causation in statistics?
5. How would you calculate the regression equation from this dataset?

**Tip:** When interpreting correlation coefficients, remember that a negative value indicates an inverse relationship, while a positive value indicates a direct relationship.

A mathematics teacher tracked the number of student absences and the students' math grades for the year. What is the correlation coefficient? Round to the nearest hundredth.

Learn how to calculate the correlation coefficient between the number of absences and math grades using Pearson's correlation formula. This problem includes a detailed step-by-step solution with real data points: absences [3, 2, 5, 1, 0, 8, 3, 2, 6] and math grades [85, 90, 65, 90, 100, 60, 80, 95, 75]. Suitable for students in Grades 10-12.

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