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Hypergeometric Mean Formula:
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The hypergeometric mean represents the expected number of successes in a sample drawn without replacement from a finite population. It's a fundamental concept in probability theory and statistics, particularly in hypergeometric distribution problems.
The calculator uses the hypergeometric mean formula:
Where:
Explanation: The formula calculates the expected value (mean) of successes when drawing n items from a population of size N containing K successes.
Details: The hypergeometric mean is crucial in quality control, ecological studies, and any scenario involving sampling without replacement. It helps predict outcomes in finite populations where each selection affects subsequent probabilities.
Tips: Enter the sample size (n), number of successes in population (K), and total population size (N). All values must be positive integers with K ≤ N and n ≤ N.
Q1: When should I use hypergeometric mean vs binomial mean?
A: Use hypergeometric when sampling without replacement from a finite population. Use binomial for sampling with replacement or from an infinite population.
Q2: What are typical applications of hypergeometric mean?
A: Common in quality control (defective items), ecological studies (species counts), and any finite population sampling scenario.
Q3: How does sample size affect the mean?
A: The mean increases linearly with sample size (n), proportionally to the success ratio (K/N) in the population.
Q4: What if my sample size equals the population?
A: When n = N, the mean equals K (total successes in population), as you've drawn all items.
Q5: Can the mean be non-integer?
A: Yes, while counts must be integers, the expected value (mean) can be fractional, representing a probabilistic average.