1. What is the Hypergeometric Distribution?

The hypergeometric distribution describes the probability of k successes in n draws without replacement from a finite population of size N containing exactly K successes. It's used when sampling without replacement from a finite population.

2. How Does the Calculator Work?

The calculator uses the hypergeometric mean formula:

Where:

• \( n \) — Sample size (number of draws)
• \( K \) — Number of successes in the population
• \( N \) — Total population size

Explanation: The mean represents the expected number of successes in the sample.

3. Importance of Hypergeometric Mean

Details: The hypergeometric mean is crucial for understanding the expected outcome in sampling without replacement scenarios, such as quality control, biological sampling, and card games.

4. Using the Calculator

Tips: Enter positive integers where n ≤ N and K ≤ N. The calculator will compute the expected number of successes in your sample.

5. Frequently Asked Questions (FAQ)

Q1: When should I use hypergeometric instead of binomial?
A: Use hypergeometric when sampling without replacement from a finite population. Use binomial when sampling with replacement or from an infinite population.

Q2: What's the difference between mean and variance?
A: The mean gives the expected value, while variance measures how far results are spread from the mean.

Q3: Can I use this for large populations?
A: Yes, but if the sample size is less than 10% of the population, binomial approximation may be sufficient.

Q4: What are common applications?
A: Quality control (defective items), ecology (species counts), and genetics (allele frequencies).

Q5: How does this relate to Fisher's exact test?
A: Fisher's exact test uses the hypergeometric distribution to calculate p-values for contingency tables.