To calculate Pearson's correlation coefficient (r), we first need to complete the table with x2, y2, and xy values for each data point, and then find the sums of all columns.

To calculate Pearson's correlation coefficient (r), we first need to complete the table with x^2, y^2, and xy values for each data point, and then find the sums of all columns. The formula for Pearson's correlation coefficient is: r = (n( xy) - ( x)( y))/(sqrt([n( x^2) - ( x)^2][n( y^2) - ( y)^2])) where n is the number of data points. In this case, n=5. Step 1: Complete the table with x^2, y^2, and xy values. | x | y | x^2 | y^2 | xy | |-----|-----|-------|-------|------| | 62 | 71 | 62^2 = 3844 | 71^2 = 5041 | 62 × 71 = 4402 | | 75 | 84 | 75^2 = 5625 | 84^2 = 7056 | 75 × 84 = 6300 | | 41 | 56 | 41^2 = 1681 | 56^2 = 3136 | 41 × 56 = 2296 | | 69 | 73 | 69^2 = 4761 | 73^2 = 5329 | 69 × 73 = 5037 | | 82 | 90 | 82^2 = 6724 | 90^2 = 8100 | 82 × 90 = 7380 | Step 2: Calculate the sums for each column. x = 62 + 75 + 41 + 69 + 82 = 329 y = 71 + 84 + 56 + 73 + 90 = 374 x^2 = 3844 + 5625 + 1681 + 4761 + 6724 = 22635 y^2 = 5041 + 7056 + 3136 + 5329 + 8100 = 28662 xy = 4402 + 6300 + 2296 + 5037 + 7380 = 25415 Step 3: Substitute these sums and n=5 into the Pearson's correlation coefficient formula. Calculate the numerator: n( xy) - ( x)( y) = 5(25415) - (329)(374) = 127075 - 123046 = 4029 Calculate the first part of the denominator under the square root: n( x^2) - ( x)^2 = 5(22635) - (329)^2 = 113175 - 108241 = 4934 Calculate the second part of the denominator under the square root: n( y^2) - ( y)^2 = 5(28662) - (374)^2 = 143310 - 139876 = 3434 Step 4: Calculate the full denominator and then r. Denominator = sqrt((4934)(3434)) Denominator = sqrt(16948356) Denominator ≈ 4116.8383 Now, calculate r: r = (4029)/(4116.8383) r ≈ 0.97866 Step 5: Round the result to three decimal places. r ≈ 0.979 This value matches option A. The final answer is A. 0.979. 3 done, 2 left today. You're making progress.