Vectorized Maths

Just like a NumPy array, a Series lets you do maths on every value at once — no loops. There are three flavours: maths with a single number, maths between two Series, and asking the Series true/false questions.

1Scalar operations (Series & a single number)

When you combine a Series with one number (a scalar), the operation is applied to every item automatically. The index stays exactly as it was.

scalar_ops.py

import pandas as pd

scores = pd.Series([10, 20, 30, 40],
                   index=['Aarav', 'Priya', 'Rohan', 'Sneha'])
print("--- Original ---")
print(scores)

print("\n--- scores + 5 ---")
print(scores + 5)

print("\n--- scores * 2 ---")
print(scores * 2)

print("\n--- scores / 10 ---")
print(scores / 10)

import pandas as pd

scores = pd.Series([10, 20, 30, 40],
                   index=['Aarav', 'Priya', 'Rohan', 'Sneha'])
print("--- Original ---")
print(scores)

print("\n--- scores + 5 ---")
print(scores + 5)

print("\n--- scores * 2 ---")
print(scores * 2)

print("\n--- scores / 10 ---")
print(scores / 10)

Tip

Try changing + 5 to ** 2 (power) or - 10 (subtraction) and re-run. Every element updates in one shot.

2Vector operations — Pandas aligns by label

When you combine two Series, Pandas doesn't just line them up top-to-bottom. It matches values by their index label. Where a label exists in both, the maths happens. Where a label is missing on either side, the result is NaN. Explore it:

How Pandas aligns two Series

Pandas matches by LABEL, not by position. A label missing on either side becomes NaN. Change the operator.

scores

Aarav10

Priya20

Rohan30

Sneha40

other_scores

Aarav5

Priya12

Vivaan20

result

Aarav15.0

Priya32.0

RohanNaN

SnehaNaN

VivaanNaN

label in both → maths happenslabel in only one → NaNA NaN makes the whole result float64 (note the .0).

First, two Series with the same labels — everything matches:

vector_matching.py

import pandas as pd

scores = pd.Series([10, 20, 30, 40],
                   index=['Aarav', 'Priya', 'Rohan', 'Sneha'])
test2  = pd.Series([8, 5, 10, 15],
                   index=['Aarav', 'Priya', 'Rohan', 'Sneha'])

print("--- Total (scores + test2) ---")
print(scores + test2)

import pandas as pd

scores = pd.Series([10, 20, 30, 40],
                   index=['Aarav', 'Priya', 'Rohan', 'Sneha'])
test2  = pd.Series([8, 5, 10, 15],
                   index=['Aarav', 'Priya', 'Rohan', 'Sneha'])

print("--- Total (scores + test2) ---")
print(scores + test2)

Now watch what happens when the labels don't line up — Rohan and Sneha are missing from the second Series, and Vivaan is new:

vector_nonmatching.py

import pandas as pd

scores = pd.Series([10, 20, 30, 40],
                   index=['Aarav', 'Priya', 'Rohan', 'Sneha'])
other  = pd.Series([5, 12, 20],
                   index=['Aarav', 'Priya', 'Vivaan'])

print(scores + other)
# Aarav & Priya match -> a number
# Rohan, Sneha, Vivaan appear in only one Series -> NaN

import pandas as pd

scores = pd.Series([10, 20, 30, 40],
                   index=['Aarav', 'Priya', 'Rohan', 'Sneha'])
other  = pd.Series([5, 12, 20],
                   index=['Aarav', 'Priya', 'Vivaan'])

print(scores + other)
# Aarav & Priya match -> a number
# Rohan, Sneha, Vivaan appear in only one Series -> NaN

Key Takeaway

Pandas aligns two Series by label, not position. A label present in only one of them produces NaN in the result.

3Boolean filtering — ask a true/false question

A comparison (>, <, ==, !=, …) turns a Series into a Series of True/False. Feed that back inside square brackets and Pandas keeps only the rows that were True — all in one line.

boolean_filter.py

import pandas as pd

scores = pd.Series([10, 20, 30, 40],
                   index=['Aarav', 'Priya', 'Rohan', 'Sneha'])

# Step 1: the condition -> a True/False Series
print("--- scores > 25 ---")
print(scores > 25)

# Step 2: use it to filter -> only the True rows survive
print("\n--- scores[scores > 25] ---")
print(scores[scores > 25])

import pandas as pd

scores = pd.Series([10, 20, 30, 40],
                   index=['Aarav', 'Priya', 'Rohan', 'Sneha'])

# Step 1: the condition -> a True/False Series
print("--- scores > 25 ---")
print(scores > 25)

# Step 2: use it to filter -> only the True rows survive
print("\n--- scores[scores > 25] ---")
print(scores[scores > 25])

Tip

Read scores[scores > 25] as "from scores, give me the items where the score is more than 25". Change 25 to 15 and re-run to see more rows survive.

Quick Check

scoresA + scoresB, where label 'Rohan' is only in scoresA. What is the result for 'Rohan'?

Quick Check

What does scores[scores > 25] return?

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🏷️ Data Types & Missing Data

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