1. What is Hypergeometric Standard Deviation?

The hypergeometric standard deviation measures the dispersion of the hypergeometric distribution, which describes the probability of k successes in n draws without replacement from a finite population.

2. How Does the Calculator Work?

The calculator uses the hypergeometric standard deviation formula:

Where:

• \( n \) — Sample size
• \( K \) — Number of successes in population
• \( N \) — Population size

Explanation: The formula accounts for sampling without replacement, with the finite population correction factor \( \frac{N - n}{N - 1} \).

3. Importance of Hypergeometric SD

Details: The standard deviation helps quantify the variability in the number of successes expected in hypergeometric experiments, useful in quality control, ecological studies, and statistical sampling.

4. Using the Calculator

Tips: Enter positive integers where n ≤ N and K ≤ N. The calculator will compute the standard deviation of the hypergeometric distribution.

5. Frequently Asked Questions (FAQ)

Q1: When should I use hypergeometric distribution?
A: Use it when sampling without replacement from a finite population, like drawing cards from a deck or defective items from a batch.

Q2: How does this differ from binomial SD?
A: Hypergeometric includes the finite population correction factor, while binomial assumes sampling with replacement or infinite population.

Q3: What are valid input ranges?
A: All values must be positive integers with n ≤ N and K ≤ N.

Q4: Can I use this for large populations?
A: For large N relative to n, the hypergeometric approaches binomial distribution.

Q5: What does a higher standard deviation indicate?
A: Greater variability in the number of successes expected across different samples.