Interactive lessons

Basic Statistics
from first principles

Each lesson is an interactive tool you can fiddle with — drag weights to shift balances, warp underlying distributions, and trace samples live to build geometric intuition before touching a formula.

Foundations & Describing Data

— 3 of 3 complete
mean (μ) median mode Balance Skew
Foundations — 01
Mean, Median, and Mode
Drag data weights along a number line. Watch the mean act as a physical fulcrum while the median tracks the absolute center file.
interactive · 2D · physics-model →
μ d² d² σ² = ∑(x-μ)²/N
Foundations — 02
Variance & Standard Deviation
Pull points away from the mean and watch literal geometric deviation squares grow. See why squaring values locks down the metric of spread.
interactive · 2D · geometry-proof →
Q2 (median) Q1 Q3
Foundations — 03
Percentiles & Box Plots
Manipulate a sorted collection of data records. Construct five-number summaries and boundary limits that reveal true distributional structure.
interactive · 2D · quartile-split →

Probability & Distributions

— 3 of 3 complete
μ +1σ −1σ 68%
Distributions — 04
The Normal Distribution
Tweak sliders for center scaling (μ) and structural spread (σ). Watch the curve continuous path reshape while locking global surface area at exactly 1.
interactive · 2D · parameters →
Z p-value Area = Prob
Distributions — 05
Probability & Area
Slide score markers across boundaries. See how integrating geometric area directly translates raw scores into standard tail probabilities.
interactive · 2D · integration →
r = +0.87
Distributions — 06
Scatter Plots & Correlation
Disperse coordinate points inside variables space. Minimize squared errors and experience how regression tracks structural linearity.
interactive · 2D · least-squares →

Inference & Testing

— 4 of 4 complete
Parent Population Sample Means (n=30) ▶ animate
Inference — 07
The Central Limit Theorem
Draw custom chaotic parent profiles. Pull samples repeatedly to reveal the standard error pathway that maps every system profile back to normality.
interactive · 2D · automated-sim →
True Mean (μ)
Inference — 08
Confidence Intervals
Shoot bracket estimators across target values. Discern process reliability metrics from specific container parameters over longitudinal sequences.
interactive · 2D · frequentist-view →
H₀ Hₐ α-crit Type I
Inference — 09
Hypothesis Testing
Shift competing distribution models across alpha lines. Balance power margins against decision errors visually before pulling static table lookups.
interactive · 2D · error-power →
H₀ (4k) Hₐ Fence Risk
Inference — 09B
Hypothesis Testing — Real World Example
Apply inference thresholds to an industrial concrete core audit. Manage consumer safety margins against supplier false alarms on a lower-tail risk field model.
interactive · 2D · left-tail · quality-control →