DISTRIBUTIONSSTARTER◉ LIVE LAB

Normal Distribution

Bell-curve averaging: many small independent effects sum to a predictable center with thin tails.

μ+σ−σ
μ center, thin tails · recreated schematic

How it works

  • Add up many small, unrelated nudges and the total piles up in the middle.
  • Spread is set by σ: ~68% within 1σ, ~95% within 2σ.
  • Standardize (z-scores) to compare apples and oranges.
Use → Use when errors aggregate. Don't use for rich-get-richer or contagious outcomes.
Watch out → Fat tails, feedback, or a handful of giants break the bell — check a histogram first.
Try it → Roll 5 dice 200 times and plot the totals: the bell appears from flat dice.
REDCAPE jobs → Reason · Predict · Communicate
Free sources → Coursera Model Thinking M2 (CLT) • OpenIntro Statistics (CC BY-SA)
INTERACTIVE LABoriginal recreation — poke it
16
Average of 1 dice, 3,000 rolls
MEAN
3.53
SPREAD (σ)
1.72

One die is flat. Average a few and a bell appears; the spread shrinks like 1/√n.