import numpy as np physics = np.array([15, 12, 8, 8, 7, 7, 7, 6, 5, 3]) history = np.array([10, 25, 17, 11, 13, 17, 20, 13, 9, 15])

n= len(physics) # num of pairs of score

calculate means

mean_physics = np.mean(physics) mean_history = np.mean(history)

calculate deviations

dev_physics = physics - mean_physics dev_history = history- mean_history

calculate the sum of product of deviations

sum_prod_dev = np.sum(dev_physics * dev_history)

calculate the sum of squared deviations

sq_dev_physics = np.sum(dev_physics**2) sq_dev_history = np.sum(dev_history**2)

calculate correlation coefficient

r = sum_prod_dev/ np.sqrt(sq_dev_physics * sq_dev_history)

print(f"Pearson's correlation coefficient: {r:.3f}")