To compute Pearson’s Product Moment Correlation (often referred to as Pearson’s $r$) for the data provided in this table, we will use the formula:

$r = \frac{\sum (X - \bar{X})(Y - \bar{Y})}{\sqrt{\sum (X - \bar{X})^2 \cdot \sum (Y - \bar{Y})^2}}$

where:

• $X$ and $Y$ represent the individual values in Data A and Data B, respectively.
• $\bar{X}$ and $\bar{Y}$ are the means of Data A and Data B.
• $\sum (X - \bar{X})(Y - \bar{Y})$ is the sum of the product of the deviations of $X$ and $Y$ from their respective means.

Step-by-Step Calculation

1. Calculate the means of Data A and Data B.
2. Calculate the deviation of each value from the mean for both Data A and Data B.
3. Multiply corresponding deviations for each pair of $X$ and $Y$.
4. Calculate the squares of each deviation for both Data A and Data B.
5. Sum the results from steps 3 and 4 to use in the Pearson formula.

Let me compute this for you.The Pearson’s Product Moment Correlation for the given data is approximately $-0.463$.

This negative correlation value suggests a moderate inverse relationship between Data A and Data B; as values in one data set tend to increase, values in the other tend to decrease to some extent.

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

Here are some related questions that could deepen your understanding:

1. How would the Pearson correlation change if all values in Data A increased by a constant amount?
2. What would a perfect positive or negative correlation look like in a dataset?
3. Can you interpret the strength of correlation based on its value? What does a weak, moderate, or strong correlation mean?
4. How does Pearson’s correlation differ from Spearman’s rank correlation?
5. Why is it important to understand the direction (positive or negative) and magnitude of a correlation?

Tip: Always visualize data when computing correlations to get a better intuitive understanding of the relationship between variables.