Bootstrap

The bootstrap is a resampling trick for measuring uncertainty without heavy formulas: you repeatedly draw new samples, with replacement, from your own data, recompute the estimate each time, and watch how much it varies. That spread approximates the sampling distribution you can never observe directly.

Its appeal is generality — it gives standard errors and confidence intervals for messy statistics (a median, a correlation, a ratio) where no neat formula exists. The honest limits: it can only reuse the information already in your sample, so it can’t fix a biased or tiny sample, and it struggles with extreme quantities like a maximum.