Questions: Calculate the correlation coefficient for the following ordered pairs. x 3 7 1 7 7 y 6 8 4 4 7 r= (Round to three decimal places as needed.)

Solution Steps

The covariance between the variables \( X \) and \( Y \) is calculated as follows:

\[ \text{Cov}(X,Y) = 2.5 \]

The standard deviation of \( X \) is given by:

\[ \sigma_X = 2.828 \]

The standard deviation of \( Y \) is given by:

\[ \sigma_Y = 1.789 \]

The correlation coefficient \( r \) is calculated using the formula:

\[ r = \frac{\text{Cov}(X,Y)}{\sigma_X \sigma_Y} \]

Substituting the values we have:

\[ r = \frac{2.5}{2.828 \times 1.789} \approx 0.494 \]

Final Answer