Bootstrap Resampling Distribution

Bootstrap Setup

Sample size (n) 30

Distribution skew 0.00

Statistic

Resamples / sec 8

Original statistic

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Bootstrap replicates (B)

Bootstrap SE

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95% CI (percentile)

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How it works

The gold spheres on the left are the original dataset X (n points drawn from a distribution you can skew). Each tick, the simulation draws a bootstrap sample X* of size n with replacement from those same n points — the pulsing spheres are the ones picked, and duplicates are allowed. It computes the chosen statistic (mean or median) of X*, and drops that value into the histogram on the right as one more bootstrap replicate. Repeated thousands of times, the histogram approximates the sampling distribution of the statistic — without any assumption about the population's true distribution.

for b = 1..B:
  X*_b = sample(X, size=n, replace=true)
  theta*_b = statistic(X*_b)
SE_boot = stdev({theta*_b})
CI_95 = [percentile_2.5, percentile_97.5] of {theta*_b}

Sample size (n) — how many original observations exist and how many are redrawn (with replacement) per bootstrap replicate.
Distribution skew — reshapes the original data generator from symmetric to heavily right- or left-skewed, which is exactly where the bootstrap earns its keep versus a plug-in normal-theory formula.
Statistic — mean or median; the median's bootstrap distribution is visibly chunkier/less smooth for small n, a real and well-known artifact.
Resamples / sec — how fast replicates accumulate; the CI and SE readouts settle as B grows into the thousands.

Real-world relevance: this nonparametric resampling is exactly how software computes standard errors and confidence intervals for statistics — like a trimmed mean, a regression coefficient, or a machine-learning model's accuracy — that have no clean textbook formula.

Original data point Sampled this draw Bootstrap histogram bar 95% CI bound

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