Consider the data below:X1721161511242719Y7366617071906884Determine Pearson's product coefficient of correlation.Group of answer choices0.27480.0755-0.07850.9371

To calculate Pearson's product coefficient of correlation, we need to follow these steps:

1. Calculate the mean of X and Y.
2. Subtract the mean from each individual value of X and Y to get the deviation.
3. Square each deviation to get the square of deviations.
4. Multiply the deviations of X and Y to get the product of deviations.
5. Sum up the squares of deviations for X and Y separately.
6. Sum up the product of deviations.
7. Divide the sum of the product of deviations by the square root of the product of the sum of squares of deviations for X and Y.

Let's calculate:

Mean of X = (17+21+16+15+11+24+27+19)/8 = 18.75 Mean of Y = (73+66+61+70+71+90+68+84)/8 = 72.875

Deviation of X = (17-18.75, 21-18.75, 16-18.75, 15-18.75, 11-18.75, 24-18.75, 27-18.75, 19-18.75) = (-1.75, 2.25, -2.75, -3.75, -7.75, 5.25, 8.25, 0.25) Deviation of Y = (73-72.875, 66-72.875, 61-72.875, 70-72.875, 71-72.875, 90-72.875, 68-72.875, 84-72.875) = (0.125, -6.875, -11.875, -2.875, -1.875, 17.125, -4.875, 11.125)

Square of deviations of X = (3.0625, 5.0625, 7.5625, 14.0625, 60.0625, 27.5625, 68.0625, 0.0625) Square of deviations of Y = (0.015625, 47.265625, 141.015625, 8.265625, 3.515625, 293.265625, 23.765625, 123.765625)

Product of deviations = (-1.750.125, 2.25-6.875, -2.75*-11.875, -3.75*-2.875, -7.75*-1.875, 5.2517.125, 8.25-4.875, 0.25*11.125) = (-0.21875, -15.46875, 32.65625, 10.78125, 14.53125, 89.90625, -40.21875, 2.78125)

Sum of squares of deviations of X = 186.5 Sum of squares of deviations of Y = 640.875 Sum of product of deviations = 94.75

Pearson's product coefficient of correlation = 94.75 / sqrt(186.5 * 640.875) = 0.9371

So, the correct answer is 0.9371.