Python Math & Statistics — Numerical Computing

Python's math and statistics modules provide mathematical functions and statistical calculations for data analysis.

Learning Objectives

• Use math module for advanced mathematical operations
• Calculate descriptive statistics with the statistics module
• Work with decimal and fraction for precision
• Apply mathematical concepts in real-world scenarios

Math Module

import math

# Constants
print(math.pi)        # 3.141592653589793
print(math.e)         # 2.718281828459045
print(math.inf)       # infinity
print(math.nan)       # Not a Number

# Basic operations
print(math.sqrt(16))       # 4.0
print(math.pow(2, 10))     # 1024.0
print(math.log(100, 10))   # 2.0
print(math.log2(256))      # 8.0
print(math.log10(1000))    # 3.0
print(math.factorial(5))   # 120
print(math.gcd(12, 8))     # 4
print(math.fsum([0.1, 0.1, 0.1, 0.1, 0.1]))  # 0.5

Trigonometry

import math

# Degrees to radians
math.radians(180)    # pi
math.degrees(math.pi)  # 180

# Trig functions (radians)
math.sin(math.pi / 2)    # 1.0
math.cos(0)               # 1.0
math.tan(math.pi / 4)    # 1.0

# Inverse trig
math.asin(1)    # pi/2
math.acos(1)    # 0
math.atan(1)    # pi/4

Statistics Module

import statistics

data = [23, 45, 12, 67, 34, 89, 23, 56]

# Central tendency
print(statistics.mean(data))      # 43.625
print(statistics.median(data))    # 39.5
print(statistics.mode([1, 1, 2, 3]))  # 1

# Dispersion
print(statistics.stdev(data))     # 24.51 (sample)
print(statistics.variance(data))  # 600.57 (sample)
print(statistics.pstdev(data))    # 22.95 (population)
print(statistics.pvariance(data)) # 526.73 (population)

# Quantiles
print(statistics.quantiles(data, n=4))  # [26.5, 39.5, 61.5]

Decimal for Precision

from decimal import Decimal, getcontext

# Float imprecision
print(0.1 + 0.2)           # 0.30000000000000004

# Decimal for exact arithmetic
a = Decimal('0.1')
b = Decimal('0.2')
print(a + b)               # 0.3

# Set precision
getcontext().prec = 50
result = Decimal(1) / Decimal(3)
print(result)  # 0.33333333333333333333333333333333333333333333333333

Fraction for Exact Ratios

from fractions import Fraction

# Exact fractions
a = Fraction(1, 3)
b = Fraction(1, 6)
print(a + b)                # 1/2
print(float(a + b))         # 0.5

# From decimal
print(Fraction(0.25))       # 1/4
print(Fraction('0.75'))     # 3/4

Key Takeaways

1. Use math for advanced math functions and constants
2. Use statistics for quick descriptive statistics
3. Use Decimal for financial/precision calculations
4. Use Fraction for exact rational arithmetic
5. math.fsum() for accurate floating-point sums