Free Finite Population Correction Calculator
Apply the finite population correction factor to adjust the standard error when sampling a significant fraction of the population.
Corrected Standard Error
2.238307
Corrected Standard Error vs Uncorrected Standard Error
How to Apply the Finite Population Correction
Formula
FPC = sqrt((N - n) / (N - 1))
Corrected SE = SE * FPC
When sampling without replacement from a finite population, the standard error is smaller than the infinite-population formula suggests. The FPC factor accounts for this. It is close to 1 when n is small relative to N, and approaches 0 as n approaches N (census).
Example Calculation
Standard error = 2.5, sample of 100 from a population of 500.
- 01Sampling fraction = 100/500 = 0.20 (20% of population)
- 02FPC = sqrt((500-100)/(500-1)) = sqrt(400/499) = sqrt(0.8016) = 0.8954
- 03Corrected SE = 2.5 * 0.8954 = 2.2384
- 04The standard error is reduced by 10.5%
Frequently Asked Questions
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