Search Ctrl K
Home / Tools
THE FEUTEX TOOLKIT

Sampling Without Replacement

Estimate the mean, variance and feasible success range when sampling without replacement.

Probability workspace● Runs in your browser
01 Your input
02 Your result
View or copy raw result data
FormulaMean = draws*success/population; Variance = draws*(success/population)*(1-success/population)*(population-draws)/(population-1); Minimum Success = max(0,draws+success-population); Maximum Success = min(draws,success)
Sources and model references

Worked example

Inputs

Population size
100 count
Success states
30 count
Draws
10 count

Expected results

Mean
3 number
Variance
1.909090909 number
Minimum Success
0 count
Maximum Success
10 count

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter the labeled inputs using consistent units.
  2. Check the stated assumptions and calculate.
  3. Review each output and compare another input scenario.

Try this example

{
  "population": 100,
  "success": 30,
  "draws": 10
}

Accuracy and scope

Uniform sampling without replacement; moments and possible range, not tail probabilities. Finite floating-point arithmetic; results can lose precision near singular or extreme inputs.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.