The math, random and statistics Modules

Three standard modules cover most everyday numeric work. math provides mathematical functions and constants, random generates pseudo-random numbers and random choices (for simulations, games, sampling and shuffling), and statistics computes averages, spread and other descriptive statistics without installing any library.

This lesson tours each module with practical examples, and explains when to use the secrets module instead of random.

The math Module

Constants math.pi, math.e, math.tau, math.inf and math.nan; rounding with floor, ceil, trunc; powers and logs with sqrt, isqrt, pow, exp, log, log10, log2; trigonometry with sin, cos, tan, radians, degrees, hypot; number theory with factorial, gcd, lcm, comb, perm; and isclose, fsum (accurate float sums) and prod.

The random Module

random() gives a float in [0, 1); uniform(a, b) a float in a range; randint(a, b) an integer including both ends; randrange(start, stop, step); choice(seq) one item; choices(seq, weights, k) with replacement; sample(seq, k) without replacement; shuffle(list) in place; gauss(mu, sigma) normally distributed values. random.seed(n) makes results reproducible — essential for tests and experiments.

random vs secrets

random is predictable by design and must never be used for passwords, tokens or OTPs. Use the secrets module: secrets.token_urlsafe(), secrets.token_hex(), secrets.choice(), secrets.randbelow().

The statistics Module

mean, fmean, median, median_low/median_high, mode, multimode, stdev and variance (sample), pstdev and pvariance (population), quantiles, correlation and linear_regression. For large datasets, NumPy and pandas are faster, but statistics is perfect for small data and scripts.

Examples

import math

print(math.pi, math.e, math.inf > 10**100)
print(math.floor(-2.5), math.ceil(-2.5), math.trunc(-2.5))
print(math.sqrt(2), math.isqrt(17), math.pow(2, 0.5))
print(math.log(math.e), math.log10(1000), math.log2(1024), math.log(8, 2))
print(round(math.cos(math.radians(60)), 3), math.degrees(math.pi), math.hypot(3, 4))
print(math.factorial(6), math.gcd(48, 18), math.lcm(4, 10), math.comb(5, 2), math.perm(5, 2))
print(0.1 + 0.2 + 0.3, math.fsum([0.1, 0.2, 0.3]), math.prod([2, 3, 4]))

3.141592653589793 2.718281828459045 True
-3 -2 -2
1.4142135623730951 4 1.4142135623730951
1.0 3.0 10.0 3.0
0.5 180.0 5.0
720 6 20 10 20
0.6000000000000001 0.6 24

import random

random.seed(42)
print(round(random.random(), 4), round(random.uniform(1, 10), 2))
print(random.randint(1, 6), random.randrange(0, 100, 5))
colors = ["red", "green", "blue", "yellow"]
print(random.choice(colors))
print(random.choices(colors, weights=[5, 1, 1, 1], k=4))
print(random.sample(range(1, 50), 6))
deck = list(range(1, 11))
random.shuffle(deck)
print(deck)

0.6394 1.23
3 35
green
['red', 'red', 'green', 'red']
[38, 28, 3, 2, 6, 14]
[3, 6, 8, 10, 7, 2, 5, 1, 9, 4]

import secrets
import string

token = secrets.token_urlsafe(16)
otp = "".join(secrets.choice(string.digits) for _ in range(6))
print(len(token) > 16, len(otp), otp.isdigit())
print(len(secrets.token_hex(8)), 0 <= secrets.randbelow(10) < 10)

True 6 True
16 True

import statistics as st

marks = [72, 85, 90, 66, 85, 78, 95, 85]
print(st.mean(marks), st.median(marks), st.mode(marks), st.multimode([1, 1, 2, 2, 3]))
print(round(st.stdev(marks), 2), round(st.pstdev(marks), 2), round(st.variance(marks), 2))
print(st.quantiles(marks, n=4))

hours = [1, 2, 3, 4, 5]
scores = [52, 60, 68, 71, 82]
print(round(st.correlation(hours, scores), 3))
slope, intercept = st.linear_regression(hours, scores)
print(round(slope, 2), round(intercept, 2), "predicted for 6h:", round(slope * 6 + intercept, 1))

82 85.0 85 [1, 2]
9.5 8.89 90.29
[73.5, 85.0, 88.75]
0.989
7.1 45.3 predicted for 6h: 87.9