Statistics & Sampling
Watch one real sample become one sample mean, then one point in a growing sampling distribution.
A deterministic browser-side visual lab for descriptive statistics and repeated sampling. The learner can play or step through draw → mean → sampling-distribution → standard-error stages while every displayed value comes from the exact local samples.
Step by step
- Choose a population shape and inspect its actual μ and σ.
- Draw one exact sample of size n from that same population.
- Calculate x̄ from the sampled values and inspect the arithmetic.
- Drop that exact x̄ into the growing sampling distribution.
- Repeat the experiment and compare empirical SE with σ/√n.
- Increase n and watch the distribution of sample means tighten.
Core formulas
Sample mean
x̄ = (1/n) Σ xᵢThe sample mean summarizes one sample.
Population variance
σ² = (1/N) Σ (xᵢ − μ)²Variance measures squared spread around the population mean.
Standard error
SE(x̄) = σ / √nThe spread of sample means shrinks as sample size grows.
When to use Statistics & Sampling
- Learning descriptive statistics before fitting a model.
- Understanding why larger samples make estimates more stable.
- Connecting a population distribution to a sampling distribution.