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Math, Random, and Statistics Modules

Python provides comprehensive mathematical, statistical, and pseudo-random number capabilities built directly into its standard library.

1. The math Module

The math module provides access to standard mathematical functions for floating-point calculations.

Common math Functions

Function Description Example Result
math.sqrt(x) Square root math.sqrt(49) 7.0
math.ceil(x) Smallest integer greater than or equal to x math.ceil(4.2) 5
math.floor(x) Largest integer less than or equal to x math.floor(4.8) 4
math.gcd(a, b) Greatest Common Divisor math.gcd(24, 36) 12
math.lcm(a, b) Least Common Multiple math.lcm(4, 6) 12
math.comb(n, k) Combinations (n choose k) math.comb(5, 2) 10
math.perm(n, k) Permutations math.perm(5, 2) 20
Example: Using math Functions
import math

print("Pi:", math.pi)
print("Euler's Number (e):", math.e)
print("Square Root of 64:", math.sqrt(64))
print("Factorial of 5:", math.factorial(5))
Output
Pi: 3.141592653589793 Euler's Number (e): 2.718281828459045 Square Root of 64: 8.0 Factorial of 5: 120

2. The random Module

The random module provides tools to generate pseudo-random numbers, make random selections, and shuffle data.

Important Random Functions

Function Description Example
random.random() Returns float between 0.0 and 1.0 random.random()
random.randint(a, b) Returns integer $N$ such that $a \le N \le b$ random.randint(1, 10)
random.choice(seq) Selects a single random item from sequence random.choice(["A", "B", "C"])
random.choices(seq, k) Picks $k$ items with replacement (duplicates possible) random.choices(["A", "B"], k=3)
random.sample(seq, k) Picks $k$ unique items without replacement random.sample(range(100), 5)
random.shuffle(lst) Shuffles list in-place random.shuffle(cards)
Example: Generating Random Values
import random

# Roll a six-sided die
die_roll = random.randint(1, 6)
print("Die Roll:", die_roll)

# Pick 3 random winners from a list
participants = ["Alice", "Bob", "Charlie", "David", "Emma"]
winners = random.sample(participants, 3)
print("Winners:", winners)

3. The statistics Module

The statistics module provides mathematical statistics functions for analyzing numeric data.

Function Description
statistics.mean(data) Arithmetic average of data
statistics.median(data) Middle value of data
statistics.mode(data) Most frequent value in data
statistics.stdev(data) Sample standard deviation
statistics.variance(data) Sample variance
Example: Computing Summary Statistics
import statistics

grades = [85, 90, 78, 92, 88, 90, 95]

print("Mean:", statistics.mean(grades))
print("Median:", statistics.median(grades))
print("Mode:", statistics.mode(grades))
print("Standard Deviation:", round(statistics.stdev(grades), 2))
Output
Mean: 88.28571428571429 Median: 90 Mode: 90 Standard Deviation: 5.56