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How to use the hypergeometric distribution calculator?

To calculate the probability of any data using hypergeometric distribution calculator, follow the below steps:
  • Enter the population size (N)
  • Enter the number of success states in population (K)
  • Enter the sample size (n)
  • Enter the number of success states in sample (k)

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Hypergeometric distribution calculator


Hypergeometric distribution calculator:


The Hypergeometric distribution calculator is used to calculate the probability of a raw data, it also calculates mean, standard deviation, and variance of the entered data according to the properties of Hypergeometric distribution.  


What is Hypergeometric distribution?


Generally, in statistics and probability theory, the hypergeometric distribution refers to a discrete probability distribution of success.


Formula of hypergeometric distribution:


To calculate the probability of success using Hypergeometric distribution, we use the following formula:

  • N is the population size
  • K is the number of successes
  • n is the number of occurrences  
  • k is the number of observed successes

Properties of Hypergeometric distribution:


There are three properties of the hypergeometric distribution

Mean:

The mean of the hypergeometric distribution can be calculated by using the following formula:

Mean of Hypergeometric distribution

  • n is the number of occurrences  
  • K is the number of successes
  • N is the population size

Standard deviation:

Standard deviation is a property of the hypergeometric distribution, it can be calculated as:

Standard deviation of Hypergeometric distribution

Variance:

The variance of hypergeometric distribution can be calculated by using the following formula:

Variance of hypergeometric distribution


Example section:


In this section, we’ll cover the step-by-step calculations of probability using the hypergeometric distribution.

Example 1:

Calculate the values of hypergeometric distribution if N = 54, K = 22, n = 17, and k = 7.

Solution:

Step 1: Calculate mean

μ = n * (K / N)

μ = 17 * 22 / 54

μ = 187/27

μ = 6.926

Step 2: Calculate variance:

σ2 = {n * (K / N)} * {(N - K) / N} * {(N - n) / (N - 1)}

σ2 = {17 * (22 / 54)} * {(54 - 22) / 54} * {(54 - 17) / (54 - 1)}

σ2 = 110704 / 38637 

σ2 = 2.8652

Step 3: Calculate the probability:

P (X = 7) ≈ 0.233327502982322

P (X < 7) ≈ 0.402610817520716

P (X <= 7) ≈ 0.635938320503037

P (X > 7) ≈ 0.364061679496963

P (X >= 7) ≈ 0.597389182479284


References:


Hypergeometric Distribution: Uses & Formula | Statistics by Jim.

Hypergeometric distribution| WallStreetMojo.

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