📐 High School Geometry (Determined)
Exact formulas operate on fixed, clean inputs. Change an angle by 1°, and the result shifts by an exact deterministic step. Zero variance, zero sample size needed.
c = √(a² + b² - 2ab·cos(θ))
Result: Exact scalar with 0 uncertainty.
Result: Exact scalar with 0 uncertainty.
🎲 Real-World Statistics (Inference)
Real systems have noise. You never measure the full population—only samples. As sample size (N) increases, the Standard Error shrinks by 1/√N.
SE = σ / √N | 95% CI = x̄ ± (1.96 · SE)
Result: Probabilistic boundary under noise.
Result: Probabilistic boundary under noise.
Canonical Experiment Summary
Draw samples to compute live empirical metrics. Notice how increasing N narrows the 95% Confidence Interval funnel and accelerates convergence toward the true mean.
{"status":"initialized","draws":0,"sample_size":30,"pop_mean":100,"sample_mean":null,"se":null}