import numpy as np

ages = np.array([14, 15, 16, 16, 16, 22, 22, 24, 24, 25, 25, 25, 25, 25])

# a

expect_j_sqrd = np.sum(ages ** 2) / len(ages)
print("<j^2>:", expect_j_sqrd)

expect_j = np.sum(ages) / len(ages)
print("<j>^2:", expect_j ** 2)

# b

unique_ages = np.unique(ages)
unique_delta_js = unique_ages - expect_j
print("delta js:", [(unique_ages[i], unique_delta_js[i]) for i in range(len(unique_ages))])

delta_js = ages - expect_j
std_eq11 = np.sqrt(np.sum(delta_js ** 2) / len(delta_js))
print("std eq. 1.11:", std_eq11)

# c

std_eq12 = np.sqrt(expect_j_sqrd - expect_j ** 2)
print("std eq. 1.12:", std_eq12)