Series arithmetic and alignment in Data Analysis Python

Introduction

We use series arithmetic and alignment to do math on data that has labels. It helps us add, subtract, or compare data even if the labels don't match exactly.

You want to add sales numbers from two different months where some products are missing in one month.

You need to subtract expenses from income for different categories that don't fully overlap.

You want to combine survey results from two groups where some questions were only asked in one group.

You want to multiply prices and quantities for items where some items are missing in one list.

Syntax

Data Analysis Python

result = series1 + series2
result = series1 - series2
result = series1 * series2
result = series1 / series2

Series are like lists with labels (indexes).

When you do arithmetic, pandas matches data by these labels automatically.

Examples

Add two series with some matching and some different labels. The result shows sums where labels match and NaN where they don't.

Data Analysis Python

import pandas as pd

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

result = s1 + s2
print(result)

Multiply two series with the same labels. The result is element-wise multiplication.

Data Analysis Python

s1 = pd.Series([5, 10, 15], index=['x', 'y', 'z'])
s2 = pd.Series([2, 4, 6], index=['x', 'y', 'z'])

result = s1 * s2
print(result)

Subtract series where one has fewer labels. Missing labels result in NaN.

Data Analysis Python

s1 = pd.Series([100, 200], index=['p', 'q'])
s2 = pd.Series([50], index=['p'])

result = s1 - s2
print(result)

Sample Program

This program adds sales numbers from January and February. It shows how pandas adds values with matching labels and puts NaN where a label is missing in one series.

Data Analysis Python

import pandas as pd

# Create two series with some overlapping and some unique labels
sales_jan = pd.Series([250, 150, 400], index=['apples', 'bananas', 'oranges'])
sales_feb = pd.Series([200, 180, 100, 300], index=['apples', 'bananas', 'pears', 'oranges'])

# Add sales from January and February
combined_sales = sales_jan + sales_feb

print(combined_sales)

Important Notes

If a label is missing in one series, the result for that label is NaN (not a number).

You can use methods like .fillna() to replace NaN with a number if needed.

Arithmetic operations align data by labels automatically, no need to sort or match manually.

Summary

Series arithmetic matches data by labels before doing math.

Results have NaN where labels don't match.

This makes combining and comparing labeled data easy and safe.

Practice

1. What happens when you add two pandas Series with different labels using + operator?

easy

A. The result is a Series with all zeros

B. Values are added ignoring labels, just by position

C. An error is raised due to label mismatch

D. Values are added only where labels match; others become NaN

Solution

1. Step 1: Understand pandas Series label alignment

   When adding two Series, pandas aligns data by their labels (index) before performing arithmetic.

2. Step 2: Effect of label mismatch on addition

   If a label is missing in one Series, the result for that label is NaN because pandas cannot add missing data.

3. Final Answer:

   Values are added only where labels match; others become NaN -> Option D

4. Quick Check:

   Series addition aligns labels = Values are added only where labels match; others become NaN [OK]

Hint: Remember: pandas adds by matching labels, not positions [OK]

Common Mistakes:

• Assuming addition ignores labels and adds by position
• Expecting an error on label mismatch
• Thinking missing labels fill with zero automatically

2. Which of the following is the correct syntax to add two pandas Series s1 and s2 with label alignment, allowing specification of fill_value for missing labels?

easy

A. s1 + s2

B. s1 + s2.values

C. s1.add(s2)

D. s1.append(s2)

Solution

1. Step 1: Check syntax for adding Series with alignment and fill_value

   Using s1.add(s2) adds Series with label alignment and allows fill_value for missing labels.

2. Step 2: Compare other options

   s1 + s2 adds with alignment but no fill_value option. s1 + s2.values ignores labels (positional). s1.append(s2) concatenates.

3. Final Answer:

   s1.add(s2) -> Option C

4. Quick Check:

   Use .add() for aligned addition with fill_value [OK]

Hint: Use .add() method for safe label-aligned addition [OK]

Common Mistakes:

• Using + with raw values ignoring labels
• Confusing append with addition
• Not knowing .add() exists for Series

3. Given the code:

import pandas as pd
s1 = pd.Series([10, 20, 30], index=['a', 'b', 'c'])
s2 = pd.Series([1, 3, 3], index=['b', 'c', 'd'])
result = s1 + s2
print(result)

What is the output?

medium

A. a NaN
b 21.0
c 33.0
d NaN

B. a 10
b 22
c 33
d 3

C. a 10
b 21
c 33
d 3

D. a NaN
b 22.0
c 33.0
d NaN

Solution

1. Step 1: Align Series by labels

   s1 has 'a':10, 'b':20, 'c':30; s2 has 'b':1, 'c':3, 'd':3. Union index: 'a','b','c','d'.

2. Step 2: Add values where labels match, NaN otherwise

   'a': 10 + NaN = NaN, 'b':20+1=21.0, 'c':30+3=33.0, 'd': NaN + 3 = NaN. Floats due to NaN.

3. Final Answer:

   a NaN b 21.0 c 33.0 d NaN -> Option A

4. Quick Check:

   Series addition aligns labels, unmatched get NaN [OK]

Hint: Add Series and check labels; unmatched labels become NaN [OK]

Common Mistakes:

• Adding values by position ignoring labels
• Expecting no NaN for unmatched labels
• Misreading index labels and values

4. Consider the code:

import pandas as pd
s1 = pd.Series([5, 10], index=['x', 'y'])
s2 = pd.Series([2, 4, 6], index=['x', 'y', 'z'])
result = s1 + s2
print(result)

The result contains NaN. What is the problem and how to fix it to treat missing values as zero?

medium

A. No error; code runs fine

B. NaN due to different lengths; fix by using s1.add(s2, fill_value=0)

C. Error because + cannot add Series; use concat instead

D. Error due to missing index in s1; fix by reindexing s1 to s2's index

Solution

1. Step 1: Check the code execution

   The code runs but produces NaN for 'z' (missing in s1). Alignment by labels causes NaN for unmatched.

2. Step 2: Fix with fill_value

   s1.add(s2, fill_value=0) fills missing labels with 0: 'x':7, 'y':14, 'z':6.

3. Final Answer:

   NaN due to different lengths; fix by using s1.add(s2, fill_value=0) -> Option B

4. Quick Check:

   Use .add() with fill_value to avoid NaN [OK]

Hint: Use .add(fill_value=0) to handle missing labels safely [OK]

Common Mistakes:

• Thinking + raises error on length mismatch
• Using concat instead of arithmetic
• Ignoring missing labels causing NaN

5. You have two Series representing sales in two stores:

store1 = pd.Series([100, 200, 300], index=['apple', 'banana', 'orange'])
store2 = pd.Series([50, 150, 100], index=['banana', 'orange', 'grape'])

How do you create a Series showing total sales per fruit, treating missing fruits as zero?

hard

A. store1.add(store2, fill_value=0)

B. store1 + store2

C. store1.append(store2).sum()

D. store1.combine(store2, lambda x, y: x + y)

Solution

1. Step 1: Understand the problem

   We want to add sales per fruit, but some fruits are missing in one store's Series.

2. Step 2: Use addition with fill_value=0

   Using store1.add(store2, fill_value=0) adds values label-wise, treating missing labels as zero, so no NaN appears.

3. Final Answer:

   store1.add(store2, fill_value=0) -> Option A

4. Quick Check:

   Add Series with fill_value=0 to handle missing labels [OK]

Hint: Use .add(fill_value=0) to sum with missing labels as zero [OK]

Common Mistakes:

• Using + causing NaN for missing labels
• Using append and sum incorrectly
• Using combine without fill_value causing NaN