Arithmetic Operations

🧮 Pandas Arithmetic Operations: Your Data’s Calculator

Imagine you have a magical calculator that can do math on thousands of numbers at once. That’s what Pandas arithmetic is!

🎯 What’s This All About?

Think of your data like a classroom full of students. Each student has a test score. What if you wanted to:

• Give everyone 5 bonus points?
• Double everyone’s score?
• Compare two classrooms?

With Pandas, you can do ALL of this with just ONE line of code! No loops, no fuss.

📊 Series Arithmetic: Math on a Single Column

A Series is like a single column of numbers — imagine a list of prices at a candy store.

The Magic: Operations Apply to EVERY Item

import pandas as pd

# Candy prices in dollars
prices = pd.Series([1.50, 2.00, 0.75, 3.25])

# Add 0.50 to EVERY price (tax!)
prices + 0.50
# Result: [2.00, 2.50, 1.25, 3.75]

# Double all prices
prices * 2
# Result: [3.00, 4.00, 1.50, 6.50]

Series + Series = Element-by-Element Math

costs = pd.Series([1.00, 1.50, 0.50, 2.00])
markup = pd.Series([0.50, 0.50, 0.25, 1.25])

# Final price = cost + markup
final_price = costs + markup
# Result: [1.50, 2.00, 0.75, 3.25]

🎪 Analogy: It’s like two lines of kids pairing up. Kid 1 from line A pairs with Kid 1 from line B. They add their candies together!

📋 DataFrame Arithmetic: Math on Tables

A DataFrame is a whole table — like a spreadsheet with rows AND columns.

Scalar Operations (One Number to All)

# Student grades
grades = pd.DataFrame({
    'Math': [85, 90, 78],
    'Science': [88, 92, 85]
})

# Curve: Add 5 points to EVERYTHING
curved = grades + 5
# Math becomes [90, 95, 83]
# Science becomes [93, 97, 90]

DataFrame + DataFrame

semester1 = pd.DataFrame({
    'Math': [80, 85],
    'Science': [75, 90]
})

semester2 = pd.DataFrame({
    'Math': [85, 90],
    'Science': [80, 88]
})

# Total points = semester1 + semester2
total = semester1 + semester2
# Math: [165, 175]
# Science: [155, 178]

🏠 Analogy: Imagine two identical houses. You’re counting windows in each room. DataFrame arithmetic lets you add up windows room-by-room, floor-by-floor, all at once!

🔧 Arithmetic Methods: The Named Tools

Sometimes using +, -, *, / isn’t enough. Pandas gives you methods with superpowers!

Basic Methods

The fill_value Superpower

What happens when data is missing? Methods let you handle it!

a = pd.Series([1, 2, None, 4])
b = pd.Series([10, 20, 30, 40])

# Regular addition: None + 30 = NaN
a + b  # [11, 22, NaN, 44]

# Using fill_value: treat None as 0
a.add(b, fill_value=0)
# [11, 22, 30, 44] ✨

🧩 Analogy: fill_value is like having a substitute player. When someone is absent, the substitute jumps in!

🚀 Advanced Arithmetic Operations

Reverse Operations

Sometimes you want number - Series instead of Series - number:

prices = pd.Series([10, 20, 30])

# Regular: prices - 5 = [5, 15, 25]
prices - 5

# Reverse: 100 - prices = [90, 80, 70]
prices.rsub(100)  # "reverse subtract"

Combining Multiple Operations

# Calculate final price with tax and discount
base_price = pd.Series([100, 200, 150])
tax_rate = 0.08
discount = 10

final = base_price.mul(1 + tax_rate).sub(discount)
# Step 1: 100 * 1.08 = 108
# Step 2: 108 - 10 = 98
# Result: [98, 206, 152]

Operations with Different Indexes

s1 = pd.Series([1, 2, 3], index=['a', 'b', 'c'])
s2 = pd.Series([10, 20, 30], index=['b', 'c', 'd'])

result = s1 + s2
# a: NaN (only in s1)
# b: 2 + 10 = 12
# c: 3 + 20 = 23
# d: NaN (only in s2)

🎭 Analogy: It’s like matching dance partners by name tags. Only people with matching tags can dance together. Everyone else sits out (NaN)!

📡 Broadcasting in Pandas

Broadcasting is Pandas’ way of being smart about mismatched shapes.

Series + Scalar (Simplest Broadcasting)

scores = pd.Series([70, 80, 90])
bonus = 5

# The single number "broadcasts" to all
scores + bonus  # [75, 85, 95]

DataFrame + Series (Column-wise)

df = pd.DataFrame({
    'A': [1, 2, 3],
    'B': [4, 5, 6]
})

row_adjustment = pd.Series([10, 100], index=['A', 'B'])

# Series broadcasts across ROWS
df + row_adjustment
# A: [11, 12, 13]
# B: [104, 105, 106]

Row-wise Broadcasting with axis=0

df = pd.DataFrame({
    'Math': [80, 90],
    'Science': [85, 88]
})

student_bonus = pd.Series([5, 10])  # Per student

# Add different bonus to each ROW
df.add(student_bonus, axis=0)
# Row 0: Math=85, Science=90
# Row 1: Math=100, Science=98

graph TD
    A["Small Shape"] --> B["Broadcasting Engine"]
    C["Large Shape"] --> B
    B --> D["Matched Shapes"]
    D --> E["Element-wise Operation"]
    E --> F["Result!"]

🎈 Analogy: Broadcasting is like a balloon that expands to fill any space. A single number “inflates” to match the bigger shape!

🎯 Quick Summary

💡 Remember This!

1. Operations apply to ALL elements — no loops needed!
2. Matching happens by index — mismatched indexes give NaN
3. Methods give you fill_value — handle missing data gracefully
4. Broadcasting is automatic — Pandas figures out the shape

You’ve just learned how to make thousands of calculations with single lines of code. That’s the power of Pandas arithmetic! 🎉