The data below are the number of hours worked (per week) and the final grades of 9 randomly selected students from a drama class. Calculate the linear correlation coefficient. \begin{tabular}{|c|c|} \hline Number of hours worked, $x$ & Final grade, $y$ \\ \hline 2 & 90 \\ \hline 5 & 78 \\ \hline 8 & 72 \\ \hline 6 & 74 \\ \hline 11 & 63 \\ \hline 4 & 84 \\ \hline 17 & 47 \\ \hline 10 & 68 \\ \hline 7 & 74 \\ \end{tabular} $-0.991$ 0.982 $-0.899$ $-0.888$

Step 1 ：Given the data of the number of hours worked (per week) and the final grades of 9 randomly selected students from a drama class, we are asked to calculate the linear correlation coefficient, also known as Pearson's correlation coefficient. This coefficient measures the strength and direction of association between two continuous variables. In this case, the two variables are the number of hours worked and the final grade.

Step 2 ：The formula for Pearson's correlation coefficient is: \[ r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}} \] where: \(x\) and \(y\) are the variables, \(n\) is the number of data points, \(\sum xy\) is the sum of the product of \(x\) and \(y\), \(\sum x\) and \(\sum y\) are the sums of \(x\) and \(y\) respectively, \(\sum x^2\) and \(\sum y^2\) are the sums of the squares of \(x\) and \(y\) respectively.

Step 3 ：Let's calculate the sums and products needed for the formula. The number of hours worked, \(x\), is [2, 5, 8, 6, 11, 4, 17, 10, 7] and the final grades, \(y\), is [90, 78, 72, 74, 63, 84, 47, 68, 74]. The number of data points, \(n\), is 9. The sum of \(x\), \(\sum x\), is 70. The sum of \(y\), \(\sum y\), is 650. The sum of the product of \(x\) and \(y\), \(\sum xy\), is 4616. The sum of the squares of \(x\), \(\sum x^2\), is 704. The sum of the squares of \(y\), \(\sum y^2\), is 48178.

Step 4 ：Substitute these values into the formula, we get \(r = -0.990782783692116\).

Step 5 ：Final Answer: The linear correlation coefficient is \(\boxed{-0.991}\). This indicates a strong negative correlation between the number of hours worked and the final grade, meaning that as the number of hours worked increases, the final grade tends to decrease.