DISTRIBUTIONSSTARTER◉ LIVE LAB
Central Limit & Six Sigma
Sample averages settle to normal; variation reduction pays until returns diminish.
How it works
- Average enough independent samples and the average goes normal.
- Bigger n shrinks wobble by √n — quadrupling halves noise.
- Six Sigma is this idea weaponized against variation.
Use → Quality programs, polling margins, A/B sizing.
Watch out → Tiny samples wearing normal-theory confidence intervals.
Try it → Average 30 coin-flip batches; watch the histogram bell up.
REDCAPE jobs → Reason · Communicate
Free sources → Coursera M2 (CLT & Six Sigma) • OpenIntro Statistics (CC BY-SA)
INTERACTIVE LABoriginal recreation — poke it
MEAN
3.53
SPREAD (σ)
1.72
One die is flat. Average a few and a bell appears; the spread shrinks like 1/√n.
Attach to a lattice — combines with
Different families, shared jobs. Disagreement between them is where insight lives.
LINEAR & NONLINEAR
Categorical & Threshold Models
Buckets and cutoffs turn messy attributes into testable if-then rules.
SHARED JOBS: REASON · COMMUNICATE
GAMESShapley Value & Power
Credit each player by their average marginal contribution across every order of joining.
SHARED JOBS: REASON · COMMUNICATE
DIFFUSIONBroadcast Model
One source reaches a fixed pool at a steady rate: fast early, then fading returns — the r-shaped curve.
SHARED JOB: COMMUNICATE
More in Distributions
Normal Distribution
Bell-curve averaging: many small independent effects sum to a predictable center with thin tails.
Power Law / Long Tail
Rich-get-richer: a few huge winners, many tiny players. Straight line on log-log.
Poisson Arrivals
Counts of rare independent events per window: calls, mutations, clicks.