Distribution Plots

🎨 Statistical Plots: Distribution Plots

Seeing How Your Data Spreads Out — Like Watching Water Flow!

🌊 The Big Picture: What Are Distribution Plots?

Imagine you have a jar full of colorful marbles. Some colors appear more often than others. Distribution plots are like magical X-ray glasses that show you:

• Which values appear most often (the popular kids!)
• Which values are rare (the shy ones hiding in corners)
• How your data spreads out from low to high

Think of it like watching water flow down a hill — distribution plots show you where the water pools (common values) and where it barely trickles (rare values).

🌈 Density Plot: The Smooth Mountain of Data

What Is a Density Plot?

A density plot is like drawing a smooth hill over your data. Instead of showing choppy bars like a histogram, it creates a beautiful flowing curve.

Simple Analogy:

• Histogram = Stacking blocks (chunky, blocky)
• Density Plot = Drawing a smooth blanket over those blocks (flowy, pretty!)

Why Use It?

• Shows the shape of your data clearly
• Great for comparing multiple groups
• No need to pick “bin sizes” like histograms

🐍 How to Create One

import matplotlib.pyplot as plt
import numpy as np
from scipy import stats

# Your data (test scores)
scores = [72, 85, 78, 92, 88, 75, 95, 82, 79, 91]

# Create the smooth curve
density = stats.gaussian_kde(scores)
x_range = np.linspace(60, 100, 200)

plt.fill_between(x_range, density(x_range), alpha=0.5)
plt.plot(x_range, density(x_range), linewidth=2)
plt.xlabel('Test Scores')
plt.ylabel('Density')
plt.title('Score Distribution')
plt.show()

🎯 Key Points

🧙‍♂️ Pro Tip

Higher peaks = more data points clustered there. Think of it as “more people standing on that spot!”

📈 ECDF Plot: The Climbing Staircase

What Is ECDF?

ECDF stands for Empirical Cumulative Distribution Function. Don’t let the fancy name scare you!

Simple Explanation: It’s like counting how many people are shorter than you as you walk through a line sorted by height.

The Staircase Analogy 🪜

Imagine everyone in your class stands in a line from shortest to tallest. As you walk past each person:

• 1 person passed = 10% done
• 5 people passed = 50% done
• Everyone passed = 100% done

The ECDF shows this as a climbing staircase!

🐍 How to Create One

import matplotlib.pyplot as plt
import numpy as np

# Heights of 10 students (in cm)
heights = [150, 155, 162, 165, 168, 170, 172, 178, 180, 185]

# Sort the data
sorted_heights = np.sort(heights)

# Create y-values (proportions)
y = np.arange(1, len(heights) + 1) / len(heights)

plt.step(sorted_heights, y, where='post', linewidth=2)
plt.xlabel('Height (cm)')
plt.ylabel('Proportion of Students')
plt.title('ECDF of Student Heights')
plt.grid(True, alpha=0.3)
plt.show()

🎯 Reading the ECDF

🪄 Magic Trick

To find the median (middle value), look where the line crosses y = 0.5 and trace down to the x-axis!

graph TD
    A["Start at y=0.5"] --> B["Draw line across"]
    B --> C["Find where it hits ECDF"]
    C --> D["Drop down to x-axis"]
    D --> E[That's your median!]

🥧 Pie Chart Basics: Slicing the Pizza!

What Is a Pie Chart?

A pie chart is exactly what it sounds like — a circle divided into slices, just like a pizza! 🍕

Each slice shows what fraction of the whole each category represents.

When to Use Pie Charts

✅ Good for:

• Showing parts of a whole
• When you have 2-5 categories
• Percentages that add up to 100%

❌ Bad for:

• Many categories (too many tiny slices!)
• Comparing precise values
• Data that doesn’t represent “parts of a whole”

🐍 How to Create One

import matplotlib.pyplot as plt

# Favorite fruits in class
fruits = ['Apples', 'Bananas', 'Oranges', 'Grapes']
votes = [8, 5, 4, 3]

plt.pie(votes, labels=fruits)
plt.title('Favorite Fruits in Class')
plt.show()

🎯 The Basic Recipe

🎨 Pie Chart Customization: Make It Beautiful!

Now let’s turn that plain pie into a masterpiece!

Adding Percentages

Show exactly how big each slice is:

import matplotlib.pyplot as plt

fruits = ['Apples', 'Bananas', 'Oranges', 'Grapes']
votes = [8, 5, 4, 3]

plt.pie(votes, labels=fruits, autopct='%1.1f%%')
plt.title('Favorite Fruits')
plt.show()

The autopct='%1.1f%%' magic adds percentages with 1 decimal place!

Exploding a Slice 💥

Want to highlight the winner? Make it “pop out”:

import matplotlib.pyplot as plt

fruits = ['Apples', 'Bananas', 'Oranges', 'Grapes']
votes = [8, 5, 4, 3]
explode = [0.1, 0, 0, 0]  # Push Apples out

plt.pie(votes, labels=fruits, explode=explode,
        autopct='%1.1f%%')
plt.title('Apples Win!')
plt.show()

Custom Colors 🌈

Pick your own color palette:

import matplotlib.pyplot as plt

fruits = ['Apples', 'Bananas', 'Oranges', 'Grapes']
votes = [8, 5, 4, 3]
colors = ['#ff6b6b', '#ffd93d', '#ff9f43', '#6c5ce7']

plt.pie(votes, labels=fruits, colors=colors,
        autopct='%1.1f%%', shadow=True)
plt.title('Colorful Fruit Chart')
plt.show()

Adding a Shadow

The shadow=True parameter adds a subtle 3D effect!

🎯 Customization Cheat Table

🎨 Start Angle Magic

Change where the first slice begins:

# Start from the top (12 o'clock position)
plt.pie(votes, labels=fruits, startangle=90)

graph TD
    A["Basic Pie"] --> B["Add Labels"]
    B --> C["Add Percentages"]
    C --> D["Add Colors"]
    D --> E["Add Explode"]
    E --> F["Add Shadow"]
    F --> G["Beautiful Chart! 🎉"]

🌟 Quick Summary

🚀 You Did It!

You now know four powerful ways to visualize how data is distributed:

1. Density plots show smooth curves of where data clusters
2. ECDF plots show cumulative stepping stones through your data
3. Pie charts slice your data like pizza
4. Customization makes your charts pop and communicate clearly

Remember: The best visualization is the one that tells your story clearly. Now go make some beautiful charts! 📊✨