1. Compute the mean of the magnitude (x) and depth (y) values.
- Sum of magnitudes: 52.01
- Sum of depths: 437.6
- Mean magnitude (\( \bar{x} \)): 52.01 / 50 = 1.0402 (rounded to 4 decimal places)
- Mean depth (\( \bar{y} \)): 437.6 / 50 = 8.752 (rounded to 3 decimal places)
2. Compute the deviations from the mean for each pair.
- Deviations for each pair (x - \( \bar{x} \)):
- (-0.29, -1.252), (-0.30, -6.252), (-0.40, 5.248), (0.16, 6.748), (-0.34, -5.752), ...
- (continuing for all 50 pairs)
- Deviations for each pair (y - \( \bar{y} \)):
- (-1.252, -1.252), (-6.252, -6.252), (5.248, 5.248), (6.748, 6.748), (-5.752, -5.752), ...
- (continuing for all 50 pairs)
3. Compute the sum of squares of the deviations.
- Sum of squares of deviations for x: 60.5431 (rounded to 4 decimal places)
- Sum of squares of deviations for y: 362.228 (rounded to 3 decimal places)
4. Compute the product of the deviations for each pair.
- Product of deviations for each pair (d_xy):
- 0.363908, 1.876176, -2.099136, 1.081568, 1.96168, ...
- (continuing for all 50 pairs)
5. Compute the sum of the products of deviations.
- Sum of products of deviations (Σd_xy): -53.919399
6. Calculate the correlation coefficient (r) using the formula:
- r = Σd_xy / sqrt((Σd_x^2)(Σd_y^2))
- r = -53.919399 / sqrt((60.5431)(362.228))
- r ≈ -53.919399 / 26.71953
- r ≈ -2.0168 (rounded to 4 decimal places)
7. Determine the critical value of r using a statistical table or software.
