Bootstrap estimation
Make the uncertainty in a small sample visible by resampling the observations themselves.
What does your sample say about uncertainty?
We have 12 synthetic observations of waiting time (minutes), with an unusually long wait in the tail. Draw new samples of 12 values with replacement from these observations. Every bar in the histogram describes a bootstrap sample mean, not an individual waiting time.
Original sample mean—
Bootstrap standard deviation—
Percentile interval—
Exact synthetic source data and numerical histogram bins
Waiting times: .
| Bootstrap mean interval | Number of replicates |
|---|
This is the simplest percentile bootstrap, conditional on a small empirical sample. The displayed endpoints vary across runs; nominal coverage is not guaranteed, especially for small, skewed datasets. Repeatedly sampling the same nonrepresentative observations also does not correct selection bias.