Data Distributions

Why Distributions Matter

Many algorithms assume data is normally distributed:

• Linear/Logistic Regression
• Naive Bayes
• PCA
• Gaussian Mixture Models

If your data is highly skewed, these algorithms perform poorly!

The Normal Distribution (Bell Curve)

μ = mean
σ = standard deviation
68% of data within ±1σ
95% of data within ±2σ
99.7% of data within ±3σ

Skewed Distributions

Right-Skewed (Positive Skew)

• Long tail on the right
• Mean > Median
• Common in: Income, house prices, wait times
• Fix: Log transform, square root transform

Left-Skewed (Negative Skew)

• Long tail on the left
• Mean < Median
• Common in: Test scores (people cluster towards 100%)
• Fix: Box-Cox transform

Bimodal & Multimodal

Multiple peaks indicate hidden groups in your data.

• Example: "Height of humans" has two peaks (men & women).
• Solution: Stratify by group or add a categorical feature.