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# Hypergeometric distribution calculator

## 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)

## 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:

• 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:

### Variance:

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

## 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.