Open a statistics textbook and you'll find a different confidence-interval formula for every situation: one for a mean, another for a median, another for a correlation, each carrying assumptions (normality, large samples) you may quietly be violating. The bootstrap replaces that whole drawer of formulas with a single, almost suspiciously simple idea, and it works for statistics that have no clean formula at all.

The one idea: your sample is your best guess at the population

You have one sample of data and you want to know how much a statistic (say, the mean) would wobble if you could collect new samples. But you can't collect new samples, you have the one.

The bootstrap's move: treat your sample as if it were the population , and draw new samples from it , with replacement. Each "resample" is the same size as your data, but some original points appear twice or thrice and others not at all.…