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HYPGEOM.DIST Function
Summary
The HYPGEOM.DIST function calculates the hypergeometric distribution, which models the probability of achieving a specific number of successes in a sample drawn without replacement from a finite population containing a known number of successes. This is essential for quality control, survey analysis, and finite population sampling scenarios.
Syntax
HYPGEOM.DIST(sample_s,number_sample,population_s,number_pop,cumulative)Parameters
| Parameter | Type | Required | Description |
|---|---|---|---|
| sample_s | Number |
Yes | Number of successes observed in the sample (integer) |
| number_sample | Number |
Yes | Total size of the sample drawn (integer) |
| population_s | Number |
Yes | Total number of successes in the entire population (integer) |
| number_pop | Number |
Yes | Total size of the population (integer) |
| cumulative | Boolean |
Yes | TRUE for cumulative distribution, FALSE for probability mass function |
Using the HYPGEOM.DIST Function
HYPGEOM.DIST is perfect for scenarios where you're sampling without replacement from a known finite population, such as quality control inspections, defect analysis, or survey sampling where the population doesn't change significantly.
Common HYPGEOM.DIST Examples
Quality Control Inspection
=HYPGEOM.DIST(1,4,8,20,TRUE)Probability of 1 or fewer defects when inspecting 4 items from a batch of 20 with 8 known defects. Returns 0.4654 (cumulative).
Exact Probability Calculation
=HYPGEOM.DIST(1,4,8,20,FALSE)Exact probability of exactly 1 defect in sample of 4 from batch of 20 with 8 defects. Returns 0.3633.
Frequently Asked Questions
Common Errors and Solutions
#NUM! error
Cause: sample_s < 0 or sample_s > MIN(number_sample, population_s)
Solution: Ensure 0 ≤ sample_s ≤ MIN(number_sample, population_s)
#NUM! error
Cause: number_sample > number_pop
Solution: Sample size cannot exceed population size
#VALUE! error
Cause: Non-numeric input
Solution: All inputs must be numbers
Notes
- All arguments truncated to integers
- Used for non-replacement sampling
- Mathematical formula: P(X=x) = [C(K,x) * C(N-K,n-x)] / C(N,n)
Compatibility
Available in: Excel 2007, Excel 2010, Excel 2013, Excel 2016, Excel 2019, Excel 2021, Microsoft 365
Not available in: Excel 2003 and earlier
Content last reviewed: December 9, 2025
Update frequency: As needed
Excel versions tested: Excel 2007+