Math and Statistics
Numerical computation is a fundamental programming skill. Python's standard library provides a full set of tools — from basic math functions to statistical analysis, from precise decimal arithmetic to fraction operations. This lesson teaches you to use the right module for the right scenario.
1. math — Mathematical Functions
PYTHON
import math
# Common constants
print(math.pi) # 3.141592653589793
print(math.e) # 2.718281828459045
# Rounding
print(math.ceil(3.14)) # 4 (ceiling)
print(math.floor(3.14)) # 3 (floor)
# Powers and logarithms
print(math.pow(2, 10)) # 1024.0 (2 to the 10th)
print(math.sqrt(16)) # 4.0 (square root)
print(math.log(100, 10)) # 2.0 (log base 10)
# Trigonometry
print(math.sin(math.pi / 2)) # 1.0
print(math.cos(0)) # 1.0
print(math.radians(180)) # 3.14159... (degrees to radians)
Example: Distance Calculation (Difficulty ⭐)
PYTHON
import math
def distance(x1, y1, x2, y2):
"""Calculate the distance between two points"""
return math.sqrt((x2 - x1) 2 + (y2 - y1) 2)
def circle_area(radius):
"""Calculate the area of a circle"""
return math.pi * radius ** 2
print(f"Distance: {distance(0, 0, 3, 4):.2f}") # 5.00
print(f"Circle area: {circle_area(5):.2f}") # 78.54
2. statistics — Statistical Analysis
PYTHON
import statistics
data = [12, 15, 18, 20, 22, 25, 30, 35, 40]
# Central tendency
print(statistics.mean(data)) # 24.11 (mean)
print(statistics.median(data)) # 22 (median)
# print(statistics.mode(data)) # mode (errors if no unique mode)
# Dispersion
print(statistics.stdev(data)) # 9.32 (sample standard deviation)
print(statistics.variance(data)) # 86.86 (sample variance)
Example: Score Analysis (Difficulty ⭐⭐)
PYTHON
import statistics
scores = [85, 92, 78, 90, 88, 76, 95, 82, 89, 73]
print("=== Score Analysis ===")
print(f"Mean: {statistics.mean(scores):.1f}")
print(f"Median: {statistics.median(scores)}")
print(f"Max: {max(scores)}")
print(f"Min: {min(scores)}")
print(f"Std Dev: {statistics.stdev(scores):.2f}")
mean = statistics.mean(scores)
std = statistics.stdev(scores)
print("\n=== Grade Distribution ===")
for score in sorted(scores, reverse=True):
if score > mean + std:
level = "Excellent ⭐"
elif score > mean:
level = "Good 👍"
elif score > mean - std:
level = "Average"
else:
level = "Needs Work 💪"
print(f" {score:3d} — {level}")
3. decimal — Precise Decimal Arithmetic
PYTHON
from decimal import Decimal, getcontext
# float precision issue
print(0.1 + 0.2) # 0.30000000000000004 ❌
# Decimal precise calculation
print(Decimal("0.1") + Decimal("0.2")) # 0.3 ✅
# Set precision
getcontext().prec = 4 # Global precision of 4 digits
print(Decimal(1) / Decimal(3)) # 0.3333 (4 digits)
# Financial calculations must use Decimal
price = Decimal("19.99")
quantity = Decimal("3")
tax_rate = Decimal("0.08")
total = price * quantity
tax = total * tax_rate
print(f"Total: {total:.2f}") # 59.97
print(f"Tax: {tax:.2f}") # 4.80
print(f"Payable: {total + tax:.2f}") # 64.77
💡 Always use
Decimal for financial calculations, never float. The 0.1 + 0.2 precision issue is fatal in finance. Decimal sacrifices some performance for precise decimal arithmetic.
4. fractions — Fraction Arithmetic
PYTHON
from fractions import Fraction
# Create fractions
f1 = Fraction(1, 3) # 1/3
f2 = Fraction(2, 6) # Auto-reduces to 1/3
print(f1) # 1/3
print(f2) # 1/3
print(f1 == f2) # True
# Fraction operations
a = Fraction(1, 2)
b = Fraction(1, 3)
print(a + b) # 5/6
print(a * b) # 1/6
print(a / b) # 3/2
# Conversion between fractions and floats
print(float(Fraction(1, 3))) # 0.3333333333
print(Fraction(0.25).limit_denominator()) # 1/4
Common Use Cases
- math: Geometry (area/volume), trigonometry, logarithmic operations.
- statistics: Exam score analysis, data reports, scientific experiment data.
- decimal: E-commerce price calculation, financial statements, tax calculation.
- fractions: Recipe proportions, engineering ratios, educational applications.
❓ FAQ
Q What's the difference between the
math module and built-in abs(), round(), sum()?A Built-in functions handle basic operations (absolute value, rounding, summation).
math provides more specialized functions (trigonometry, logarithms, factorial). Use built-ins when they suffice.
Q: Is statistics.mean() any better than manually computing the average? A: mean() is optimized internally (one pass for both sum and count), performs better for large datasets, and handles edge cases like empty lists.
Q: When should I use Fraction vs Decimal? A: Use Fraction when you need exact rational arithmetic (like fraction exercises in educational software). Use Decimal for decimal calculations with controlled precision (like finance). For simple cases, float is fine — 99% of daily programming won't need either of these.📖 Summary
math:ceil()/floor()rounding,sqrt()square root,pi/econstants, trigonometric functionsstatistics:mean()average,median()median,stdev()standard deviationDecimal: Precise decimal arithmetic, suitable for finance; create from strings (Decimal("0.1"))Fraction: Exact fraction arithmetic, auto-reduction
📝 Exercises
-
Basic (Difficulty ⭐): Use the
mathmodule to calculate the area and circumference of a circle with radius 7. -
Intermediate (Difficulty ⭐⭐): Given
data = [23, 45, 67, 12, 34, 56, 78, 90, 11, 43], usestatisticsto calculate mean, median, and standard deviation. Then usemathto determine which values fall within "mean ± standard deviation." -
Challenge (Difficulty ⭐⭐⭐): Write a "shopping cart checkout" program. Products have names, unit prices (
Decimal), and quantities. After adding items, calculate the total, tax (8%), and discount (subtract 10 for every 100), then output the final amount. Requirement: All monetary calculations must useDecimal.