Data Compression & Analysis

📦 Data Compression & Analysis

Part 1 of 7 — Lossless vs Lossy, Compression Techniques, and Data Analysis

Why Compress Data?

Smaller files mean:

• Faster transmission over networks
• Less storage space needed
• Lower bandwidth usage
• Faster loading for users

Lossless vs Lossy Compression

Lossless Example: Run-Length Encoding

Original:  AAABBBCCDDDDDD
Compressed: 3A3B2C6D

The original can be perfectly reconstructed from the compressed version.

Lossy Example: JPEG Compression

A photograph has millions of color values. JPEG removes subtle color differences that human eyes cannot easily detect. The file shrinks dramatically, but the removed data cannot be recovered.

🔑 Lossless = perfect reconstruction. Lossy = smaller file but permanent data loss. Choose based on whether quality loss is acceptable.

Concept Check 🎯

Data Analysis and Visualization

Extracting Patterns from Data

When working with large datasets, visualization reveals patterns that raw numbers cannot.

Filtering and Transforming Data

// Filter: Keep only rows where score > 80
// Sort: Order by date ascending
// Aggregate: Calculate average score per student

Interpreting Results

• Look for trends (increasing, decreasing, stable)
• Identify outliers (values far from the norm)
• Check for clusters (groups of similar data points)
• Be cautious of bias in data collection

Challenges with Large Datasets

• Storage: Require significant space
• Privacy: May contain sensitive personal information
• Accuracy: Errors are amplified at scale
• Bias: If collection methods are biased, conclusions will be skewed

Applied Recall ✍️

1. Compression that can perfectly restore the original data is called _______ compression.

2. MP3 audio files use _______ compression, permanently removing some frequencies.

3. A chart that shows the relationship between two variables using dots is called a _______ plot.

Classify the Compression 🔍

AP Exam Strategy: Data Compression & Analysis

• Know the difference: lossless (ZIP, PNG) vs lossy (JPEG, MP3, MP4)
• Lossless for critical data (medical, legal, code). Lossy for media where small quality loss is acceptable
• Run-length encoding is the lossless technique the AP exam expects you to understand
• Data analysis questions test your ability to interpret visualizations and identify patterns
• Correlation does not imply causation — always consider confounding variables
• Large datasets can reveal patterns but also amplify errors and privacy concerns

AP-Style Application 🎯

🗜️ Data Compression & Analysis

Part 2 of 7 — Key Processes

Compression: Same Information, Fewer Bits

Compression takes a sequence of bits and produces a shorter sequence that decodes back to the original (lossless) or to an approximation of it (lossy).

Concept Check 🎯

Why Lossless Has A Limit

There's an information-theoretic minimum (entropy) for lossless compression. A truly random file cannot be losslessly compressed below its original size.

A simple example: a 100-character string of alternating "AB" patterns can be encoded as "AB × 50" — far smaller. A 100-character string of random characters has no pattern to exploit.

Why Lossy Can Go Further

Lossy compression exploits human perception:

• Audio: humans don't hear above ~20 kHz; some bands can be discarded.
• Image: small color shifts in textures are imperceptible.
• Video: most pixels barely change between frames; encode the difference.

A Tiny Lossless Example: Run-Length Encoding

🗜️ Data Compression & Analysis

Part 3 of 7 — Patterns & Examples

Common Compression Patterns

Concept Check 🎯

Dictionary Coding: A Mini-Walkthrough

Imagine encoding "the cat sat on the mat":

• Build a dictionary as you go.
• Replace repeated phrases with references.

After processing once, "the " might be code 0; "at" might be code 1. The compressed stream uses these short codes for repeated phrases.

This is the core idea behind ZIP, GZIP, PNG, and most modern lossless coders.

Huffman Coding In One Picture

If a text uses A 50%, B 25%, C 12.5%, D 12.5%:

🗜️ Data Compression & Analysis

Part 4 of 7 — Connections & Interactions

Compression Connects To Other Topics

Concept Check 🎯

Big Files Demand Streaming Algorithms

When a file doesn't fit in memory, you need algorithms that process data in a single pass with constant or sub-linear memory:

This connects compression-era data sizes to algorithm design.

🗜️ Data Compression & Analysis

Part 5 of 7 — Change Over Time

How Compression Has Evolved

Concept Check 🎯

Codec Generations Roughly Halve File Sizes

🗜️ Data Compression & Analysis

Part 6 of 7 — Problem-Solving Workshop

Compression Workshop

Apply compression vocabulary to estimation and design problems.

Concept Check 🎯

Worked: Image Sizing

Worked: Audio Sizing

Worked: Choosing A Format

🗜️ Data Compression & Analysis

Part 7 of 7 — AP Review

AP Exam Recap — Compression & Analysis

Final review.

Concept Check 🎯

Final Vocab

Common Pitfalls

• Saying "compression makes data smaller" without distinguishing lossless vs lossy.
• Encrypting before compressing.
• Treating storage as the only constraint (bandwidth often matters more).
• Using lossy formats for archival or medical records.
• Ignoring openness / licensing of codecs.