To calculate Pearson’s product-moment correlation coefficient (r), you can follow this formula:

[ r = \frac{n(\Sigma xy) - (\Sigma x)(\Sigma y)}{\sqrt{[n\Sigma x^2 - (\Sigma x)^2][n\Sigma y^2 - (\Sigma y)^2]}} ]

Where:

• $x$ represents values from Data A,
• $y$ represents values from Data B,
• $n$ is the number of data points (in this case, 10),
• $\Sigma xy$ is the sum of the products of corresponding x and y values,
• $\Sigma x^2$ is the sum of the squares of x values,
• $\Sigma y^2$ is the sum of the squares of y values.

Let's go step-by-step to compute each component.

Data A: 34, 43, 32, 56, 34, 35, 46, 23, 23, 34
Data B: 15, 19, 12, 29, 12, 13, 23, 10, 9, 13

1. Compute the sum of Data A and Data B ($\Sigma x$ and $\Sigma y$).
2. Compute the sum of squares of Data A and Data B ($\Sigma x^2$ and $\Sigma y^2$).
3. Compute the product of corresponding values in Data A and Data B ($\Sigma xy$).
4. Plug the values into the formula.

Let me calculate this for you.The Pearson’s product-moment correlation coefficient (r) for the given data is approximately 0.966.

This value indicates a strong positive correlation between Data A and Data B, meaning that as the values in Data A increase, the values in Data B also tend to increase.

Would you like more details on this, or do you have any questions?

Here are five follow-up questions related to correlation and statistics:

1. What is the significance of a strong positive correlation in real-world data?
2. How does Pearson’s correlation differ from Spearman’s rank correlation?
3. Can you explain the assumptions underlying Pearson’s correlation coefficient?
4. How do outliers affect Pearson’s correlation coefficient?
5. How can you interpret correlation in terms of causality?

Tip: Always remember that correlation does not imply causation—other factors might be influencing the relationship between variables.