Interactive Lab · Data Analysis & EDA

Before you model anything, look at your data.

Its shape tells you what the summary numbers hide. A single "average" can quietly lie to you, pulled around by a long tail or one freak value, while the median barely flinches. Below is a synthetic sample you can bend at will. Drag the knobs, drop in an outlier, and watch the mean chase the tail while the median holds its ground.

🎬 Watch the 90-second explainer, then bend the shape and watch the numbers below ↓

▶ The playground, bend the shape, watch the numbers react

mean (chases the tail) median (holds its ground)

mean = 0.00median = 0.00std = 0.00skewness = 0.00n = 600

Skew 0.0

left tail ◀symmetric▶ right tail

Spread σ 1.0

0.3 · tightwide · 3.0

Sample size n 600

20 · noisysmooth · 4000

🧭 Where this fits

Knowing a distribution's shape, and when the mean lies, is the first skill of data work: latency is long-tailed (report p99, not average), income is skewed (report median), and A/B metrics need the right summary or the decision flips. The billionaire-in-the-room effect you just saw ships wrong dashboards every day.

The code that's actually running

🔮 Predict, then test

Skew the distribution hard to the right, then hit 💥 Add an outlier, a lone giant value, like one billionaire in a room of ordinary earners. Before you look: which moves more, the mean or the median? And if you had to report a single "typical" value for skewed income data, which of the two would you trust?

The takeaway

Your new mental model of a distribution

Distributions have shape, symmetry, spread, and tails. Never trust a single summary number blindly; two datasets with the same mean can look nothing alike.
The mean is fragile. Skew pulls it toward the long tail, and one outlier can drag it anywhere. It answers "where's the center of mass?", not "what's typical?"
The median is robust. It's just the middle value, half above, half below, so a freak point or a heavy tail barely moves it. That's why income and house prices are reported as medians.
Std measures spread, the average distance from the mean, but it's fragile too: outliers inflate it fast because the distances are squared.
Always plot your data before modeling. The histogram reveals the shape, skew, tails, gaps, second peaks, that no average, alone, can show you.

📖 Read the lecture notes Try: Bayes & Base Rates Continue the journey →