The product moment correlation or the Karl Pearson’s measure of correlation is given by_______.

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

The correct answer is Option 4: \[ r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n \sum x^2 - (\sum x)^2][n \sum y^2 - (\sum y)^2]}} \]

The product-moment correlation or the Karl Pearson’s measure of correlation is given by the following 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:
- \( r \) = Pearson correlation coefficient
- \( n \) = number of data points
- \( x \) = values of the first variable
- \( y \) = values of the second variable
- \( \sum xy \) = sum of the product of paired scores
- \( \sum x \) = sum of the \( x \) values
- \( \sum y \) = sum of the \( y \) values
- \( \sum x^2 \) = sum of the squared \( x \) values
- \( \sum y^2 \) = sum of the squared \( y \) values