🧩 What is Crosstab?

pandas.crosstab() is a frequency table tool that summarizes the relationship between two or more categorical variables.
It counts occurrences of combinations of categories — similar to a pivot table, but specifically for categorical comparison.

Think of it as a quick way to analyze relationships between variables like gender vs. survival, class vs. embarkation point, or smoker vs. day in a restaurant dataset.

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🔹 Syntax

pd.crosstab(index, columns, values=None, aggfunc=None, margins=False, normalize=False)

Parameters:

• index: array or Series — values to group by on the rows
• columns: array or Series — values to group by on the columns
• values: array or Series — optional values to aggregate
• aggfunc: function (like np.sum, np.mean)
• margins: True/False — adds row and column totals
• normalize: Normalizes counts (proportions or percentages)

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🧩 When Should You Use Crosstab?

Use crosstab() when you want to:

✅ Summarize categorical data
✅ Compare distributions between variables
✅ Analyze relationships between categories (e.g., gender and survival rate)
✅ Quickly compute two-way or multi-way frequency tables

Common use cases:

• Gender vs. Survival — Were women more likely to survive?
• Class vs. Embarkation Port — Which class boarded from which port?
• Age Group vs. Survival — Which age group survived more?

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🧩 Example: Titanic Dataset

Let’s load the Titanic dataset from Seaborn and explore.

import pandas as pd
import seaborn as sns

# Load dataset
titanic = sns.load_dataset('titanic')

# Display first few rows
print(titanic.head())

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🧠 Dataset Overview

Column	Description
survived	0 = No, 1 = Yes
pclass	Passenger class (1st, 2nd, 3rd)
sex	Gender
age	Age in years
sibsp	# of siblings/spouses aboard
parch	# of parents/children aboard
fare	Ticket fare
embarked	Port of embarkation (C, Q, S)
class	Class label (First, Second, Third)
who	Man, woman, or child
deck	Deck letter
embark_town	Town of embarkation
alone	True/False — if traveling alone

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🧩 Example 1 — Count of Survivors by Gender

pd.crosstab(titanic['sex'], titanic['survived'])

Output:

survived	0	1
female	81	233
male	468	109

✅ Interpretation:
Out of all females, 233 survived while 81 did not.
Among males, survival count was much lower (only 109 survived).
→ This confirms that females had a much higher survival rate.

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🧩 Example 2 — Add Margins (Totals)

pd.crosstab(titanic['sex'], titanic['survived'], margins=True)

Output:

survived	0	1	All
female	81	233	314
male	468	109	577
All	549	342	891

✅ Adds totals for both rows and columns — similar to “Grand Totals” in Excel Pivot Tables.

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🧩 Example 3 — Crosstab Between Class and Survival

pd.crosstab(titanic['class'], titanic['survived'])

survived	0	1
First	80	136
Second	97	87
Third	372	119

✅ Clearly, first-class passengers had the highest survival rates.

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🧩 Example 4 — Normalized Crosstab (Proportions)

You can normalize results to get proportions instead of counts.

pd.crosstab(titanic['sex'], titanic['survived'], normalize='index')

survived	0	1
female	0.2579	0.7421
male	0.8117	0.1883

✅ Interpretation:

• 74% of females survived
• Only 18% of males survived

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🧩 Example 5 — Multi-variable Crosstab

Let’s analyze survival based on both gender and class.

pd.crosstab([titanic['sex'], titanic['class']], titanic['survived'])

sex	class	0	1
female	First	3	91
female	Second	6	70
female	Third	72	72
male	First	77	45
male	Second	91	17
male	Third	300	47

✅ Shows a detailed breakdown — e.g., 91 first-class females survived, only 47 third-class males survived.

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🧩 Example 6 — Crosstab with an Aggregation Function

You can include a numeric column (values) and an aggregation function (aggfunc) to compute statistics.

Example: Average fare by class and survival.

pd.crosstab(
    titanic['class'],
    titanic['survived'],
    values=titanic['fare'],
    aggfunc='mean'
)

survived	0	1
First	64.68	95.12
Second	19.49	22.05
Third	13.30	13.68

✅ Interpretation:
Survivors generally paid higher fares, especially in first class.

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🧩 Example 7 — Crosstab with normalize='columns'

Normalize column-wise to see proportions per survival outcome.

pd.crosstab(titanic['sex'], titanic['survived'], normalize='columns')

survived	0	1
female	0.1475	0.6813
male	0.8525	0.3187

✅ 68% of all survivors were female.

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🧩 Example 8 — Using Multiple Columns for Index and Columns

Let’s explore how class and embark_town relate to survival.

pd.crosstab(
    [titanic['class'], titanic['embark_town']],
    titanic['survived'],
    margins=True
)

class	embark_town	0	1	All
First	Cherbourg	10	60	70
First	Queenstown	1	2	3
First	Southampton	69	74	143
Second	Cherbourg	8	15	23
Second	Queenstown	7	3	10
Second	Southampton	82	69	151
Third	Cherbourg	28	21	49
Third	Queenstown	47	7	54
Third	Southampton	297	91	388
All	All	549	342	891

✅ This gives a detailed breakdown of survival per class and boarding port.

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🧩 Example 9 — Crosstab Visualization

Crosstabs can be visualized as heatmaps for better understanding.

import seaborn as sns
import matplotlib.pyplot as plt

ct = pd.crosstab(titanic['class'], titanic['survived'], normalize='index')

sns.heatmap(ct, annot=True, cmap='coolwarm')
plt.title("Survival Rate by Passenger Class")
plt.ylabel("Passenger Class")
plt.xlabel("Survived")
plt.show()

✅ The heatmap visually shows which classes had higher survival rates.

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🧩 Summary

Concept	Description	Example
pd.crosstab()	Create frequency tables	pd.crosstab(df['A'], df['B'])
margins=True	Adds totals	pd.crosstab(A,B,margins=True)
normalize='index'	Row-wise percentage	normalize='index'
normalize='columns'	Column-wise percentage	normalize='columns'
values + aggfunc	Aggregate numeric data	values=df['fare'], aggfunc='mean'
Multiple levels	Multi-variable grouping	pd.crosstab([A,B],C)

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✅ Key Takeaways

• pd.crosstab() is perfect for categorical analysis and summarization.
• Use it for comparing variables like gender, class, or survival.
• Combine it with margins and normalize for deeper insights.
• You can even aggregate numeric values (e.g., mean fare).
• Great for exploratory data analysis (EDA) and reporting.