Operators

Mastering Python's Computational Language — From Arithmetic to Logic

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Operator Overview

Operators are symbols that perform specific operations. Python has the following operator categories:

Category	Examples	Purpose
Arithmetic operators	+, -, *, /	Mathematical calculations
Comparison operators	==, !=, >, <	Compare values
Logical operators	and, or, not	Logical judgments
Assignment operators	=, +=, -=	Variable assignment
Membership operators	in, not in	Check membership

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Arithmetic Operators

Basic Operations

a = 10
b = 3

print(a + b)   # 13  addition
print(a - b)   # 7   subtraction
print(a * b)   # 30  multiplication
print(a / b)   # 3.333... division (result is float)
print(a // b)  # 3   floor division (rounds down)
print(a % b)   # 1   modulus (remainder)
print(a ** b)  # 1000 exponentiation (10 to the power of 3)

Stata/R Comparison

Operation	Python	Stata	R
Addition	a + b	a + b	a + b
Subtraction	a - b	a - b	a - b
Multiplication	a * b	a * b	a * b
Division	a / b	a / b	a / b
Floor division	a // b	floor(a/b)	a %/% b
Modulus	a % b	mod(a, b)	a %% b
Exponentiation	a ** b	a^b	a^b or a**b

Practical Example: Income Tax Calculation

# Annual income
annual_income = 85000

# Progressive tax rates
if annual_income <= 50000:
    tax = annual_income * 0.10
elif annual_income <= 100000:
    tax = 50000 * 0.10 + (annual_income - 50000) * 0.20
else:
    tax = 50000 * 0.10 + 50000 * 0.20 + (annual_income - 100000) * 0.30

tax_rate_effective = (tax / annual_income) * 100
net_income = annual_income - tax

print(f"Annual income: ${annual_income:,}")
print(f"Tax owed: ${tax:,.2f}")
print(f"Effective tax rate: {tax_rate_effective:.2f}%")
print(f"After-tax income: ${net_income:,.2f}")

Output:

Annual income: $85,000
Tax owed: $12,000.00
Effective tax rate: 14.12%
After-tax income: $73,000.00

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Comparison Operators

Comparison operators return boolean values (True or False).

x = 10
y = 20

print(x == y)  # False  equal to
print(x != y)  # True   not equal to
print(x > y)   # False  greater than
print(x < y)   # True   less than
print(x >= y)  # False  greater than or equal to
print(x <= y)  # True   less than or equal to

Note: = vs ==

# = is assignment
age = 25

# == is comparison
is_adult = (age == 18)  # False

Practical Example: Filter Respondents

# Respondent data
age = 35
income = 75000
education_years = 16

# Filter criteria: 25-45 years old, income $50k-$100k, at least bachelor's
is_target_group = (
    (age >= 25 and age <= 45) and
    (income >= 50000 and income <= 100000) and
    (education_years >= 16)
)

print(f"Target group: {is_target_group}")  # True

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Logical Operators

Logical operators combine multiple conditions.

1. and (AND) - All conditions must be true

age = 30
has_job = True

is_eligible = (age >= 18) and has_job
print(is_eligible)  # True (both conditions met)

# If any is False, result is False
is_eligible = (age >= 50) and has_job
print(is_eligible)  # False

Truth Table:

A	B	A and B
True	True	True
True	False	False
False	True	False
False	False	False

2. or (OR) - At least one condition must be true

has_bachelors = True
has_masters = False

has_degree = has_bachelors or has_masters
print(has_degree)  # True (at least one is true)

# Both must be False for result to be False
has_degree = (has_bachelors == False) or (has_masters == False)
print(has_degree)  # True

Truth Table:

A	B	A or B
True	True	True
True	False	True
False	True	True
False	False	False

3. not (NOT) - Negation

is_student = False
is_employed = not is_student
print(is_employed)  # True

# Double negation
is_student = True
is_not_student = not is_student  # False
is_student_again = not is_not_student  # True

Combined Usage

# Complex condition: filter unemployed youth or high earners
age = 25
is_employed = False
income = 120000

is_target = (age < 30 and not is_employed) or (income > 100000)
print(is_target)  # True

Stata/R Comparison

Operation	Python	Stata	R
AND	and	&	& or &&
OR	or	`	`
NOT	not	!	!

Stata Example:

* Stata
gen is_eligible = (age >= 18 & age <= 65) & (income > 0)

R Example:

# R
is_eligible <- (age >= 18 & age <= 65) & (income > 0)

Python Example:

# Python
is_eligible = (age >= 18 and age <= 65) and (income > 0)

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Assignment Operators

Basic Assignment

x = 10  # Basic assignment

Compound Assignment Operators

x = 10

x += 5   # Equivalent to x = x + 5   → 15
x -= 3   # Equivalent to x = x - 3   → 12
x *= 2   # Equivalent to x = x * 2   → 24
x /= 4   # Equivalent to x = x / 4   → 6.0
x //= 2  # Equivalent to x = x // 2  → 3.0
x %= 2   # Equivalent to x = x % 2   → 1.0
x **= 3  # Equivalent to x = x ** 3  → 1.0

print(x)  # 1.0

Practical Example: Cumulative Calculation

# Calculate total score
total_score = 0

# Add scores incrementally
total_score += 85  # Math score
total_score += 92  # English score
total_score += 78  # Physics score

print(f"Total score: {total_score}")  # Total score: 255

# Calculate average
total_score /= 3
print(f"Average score: {total_score:.2f}")  # Average score: 85.00

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Membership Operators

in and not in

# Check if element is in sequence
majors = ['Economics', 'Sociology', 'Political Science']

print('Economics' in majors)  # True
print('Physics' in majors)    # False
print('Physics' not in majors)  # True

# Check substring
email = "alice@university.edu"
print('@' in email)  # True
print('university' in email)  # True

Practical Example: Major Classification

# Social science majors list
social_science_majors = [
    'Economics', 'Sociology', 'Political Science',
    'Psychology', 'Anthropology'
]

# Check student major
student_major = 'Economics'

if student_major in social_science_majors:
    print(f"{student_major} is a social science major")
else:
    print(f"{student_major} is not a social science major")

# Output: Economics is a social science major

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Operator Precedence

From highest to lowest:

1. () parentheses
2. ** exponentiation
3. *, /, //, % multiplication and division
4. +, - addition and subtraction
5. ==, !=, >, <, >=, <= comparison
6. not logical NOT
7. and logical AND
8. or logical OR

Examples

# Complex expression
result = 2 + 3 * 4 ** 2 > 50 and not False
# Evaluation order:
# 1. 4 ** 2 = 16
# 2. 3 * 16 = 48
# 3. 2 + 48 = 50
# 4. 50 > 50 = False
# 5. not False = True
# 6. False and True = False
print(result)  # False

# Use parentheses for clarity
result = ((2 + 3) * 4) ** 2 > 50 and (not False)
# 1. 2 + 3 = 5
# 2. 5 * 4 = 20
# 3. 20 ** 2 = 400
# 4. 400 > 50 = True
# 5. not False = True
# 6. True and True = True
print(result)  # True

Recommendation: Use parentheses to make precedence explicit in complex expressions!

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Practical Case: Data Quality Check

# Respondent data
respondent_id = 1001
age = 35
gender = "Male"
income = 75000
education_years = 16
marital_status = "Married"

# === Data quality checks ===

# 1. Age validity (18-100 years)
is_age_valid = 18 <= age <= 100

# 2. Gender validity
valid_genders = ["Male", "Female", "Other"]
is_gender_valid = gender in valid_genders

# 3. Income validity (non-negative and not too high)
is_income_valid = 0 <= income <= 10000000

# 4. Education years validity (0-30 years)
is_education_valid = 0 <= education_years <= 30

# 5. Marital status validity
valid_marital = ["Single", "Married", "Divorced", "Widowed"]
is_marital_valid = marital_status in valid_marital

# === Overall judgment ===
is_data_valid = (
    is_age_valid and
    is_gender_valid and
    is_income_valid and
    is_education_valid and
    is_marital_valid
)

# === Output report ===
print(f"Respondent {respondent_id} data quality check:")
print(f"  Age: {'✓' if is_age_valid else '✗'}")
print(f"  Gender: {'✓' if is_gender_valid else '✗'}")
print(f"  Income: {'✓' if is_income_valid else '✗'}")
print(f"  Education: {'✓' if is_education_valid else '✗'}")
print(f"  Marital: {'✓' if is_marital_valid else '✗'}")
print(f"  Overall: {'✓ Pass' if is_data_valid else '✗ Fail'}")

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Common Errors

Error 1: Confusing = and ==

age = 25      # Assignment
if age = 25:  # SyntaxError
if age == 25: # Comparison

Error 2: Misunderstanding Chained Comparisons

# Python supports chained comparisons (very convenient!)
age = 30
result = 18 <= age <= 65  # True (equivalent to age >= 18 and age <= 65)

# Don't write like this (syntax error)
result = age >= 18 and <= 65  # SyntaxError

Error 3: Logical Operator Typo

result = True && False  # SyntaxError (this is JavaScript syntax)
result = True and False # Python uses 'and'

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Practice Exercises

Exercise 1: BMI Calculation and Classification

# Given data
height_cm = 175
weight_kg = 70

# Tasks:
# 1. Calculate BMI (weight / (height_m ** 2))
# 2. Determine classification:
#    - BMI < 18.5: Underweight
#    - 18.5 <= BMI < 25: Normal
#    - 25 <= BMI < 30: Overweight
#    - BMI >= 30: Obese

Exercise 2: Complex Filter Conditions

# Given data
age = 28
income = 65000
education = "Bachelor's"
has_job = True
city = "Beijing"

# Task: Filter people who meet the following criteria
# 1. Age between 25-35
# 2. Income between $50k-$100k
# 3. At least bachelor's degree OR employed
# 4. Lives in tier-1 city (Beijing, Shanghai, Guangzhou, Shenzhen)

Exercise 3: Data Validation

# Given survey data
q1_age = 25
q2_income = -5000  # Possibly erroneous
q3_satisfaction = 7  # Satisfaction (1-5)
q4_email = "alice.example.com"  # Missing @

# Task: Check if each question's data is valid
# 1. Age: 18-100
# 2. Income: >= 0
# 3. Satisfaction: 1-5
# 4. Email: contains @

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Next Steps

In the next section, we'll learn conditional statements (if-else), using the operators we learned today for decision-making.

Keep moving forward!