Bootstrap Confidence Interval Calculator

Work out bootstrap confidence interval instantly with clear inputs, formula shown and shareable results.

About Bootstrap Confidence Interval Calculator

The bootstrap resamples the data with replacement to estimate the sampling distribution of a statistic. For the mean the resampling standard error converges to s·√((n−1)/n)/√n, which is what this reports analytically.

Formula

Bootstrap standard error of the mean

SE* = (s/√n)·√((n − 1)/n)

Worked example

With the default values below, Bootstrap Confidence Interval Calculator returns Bootstrap standard error of 2.64427448. Change any input above and every figure here is recalculated in your browser.

Inputs used

Sample data: 12, 15, 18, 22, 25, 28, 31, 35
Confidence levelaccepts 50–99.99 %: 95 %

Results

Bootstrap standard error: 2.64427448
Sample mean: 23.250000
Lower bound: 18.067317
Upper bound: 28.432683

Step by step

1Values used
2Bootstrap standard error of the mean
3Bootstrap standard error= 2.64427448
4Sample mean= 23.250000
5Lower bound= 18.067317
6Upper bound= 28.432683

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why use the bootstrap?

It needs no distributional assumption, so it works for medians, quantiles and other statistics with no simple formula.

How many resamples are needed?

A thousand suffices for standard errors, but percentile intervals in the tails usually want ten thousand or more.