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**Education Calculators** ▶ Hypergeometric Calculator

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The hypergeometric calculator is a smart tool that allows you to calculate individual and cumulative hypergeometric probabilities. Apart from it, this hypergeometric calculator helps to calculate a table of the probability mass function, upper or lower cumulative distribution function of the hypergeometric distribution, draws the chart, and also finds the mean, variance, and standard deviation of the hypergeometric distribution.

Well, before knowing about this hypergeometric distribution calculator, let’s start with the definition of hypergeometric distribution.

Specifically, a hypergeometric distribution is said to be a probability distribution that simply represents the probabilities that are associated with the number of successes in a hypergeometric experiment. You can try this hypergeometric calculator to figure out hypergeometric distribution probabilities instantly.

Let’s elaborate it with an example:

Suppose that you randomly selected 5 cards from an ordinary deck of playing cards, here you might ask: what’s the probability distribution form the number of red cards in our selection. In this example, selecting a red card would be referred to as a success. Well, the probabilities associated with each possible outcome are an example of a hypergeometric distribution, as shown in the given chart:

Outcome |
Hypergeo Prob |
Cumu Prob |

0 red cards | 0.025 | 0.025 |

1 red card | 0.150 | 0.175 |

2 red cards | 0.325 | 0.500 |

3 red cards | 0.325 | 0.825 |

4 red cards | 0.150 | 0.975 |

5 red cards | 0.025 | 1.00 |

By given this probability distribution, you can depict at a glance that the cumulative and individual probabilities are being associated with any outcome. For instance, the cumulative probability of selecting 1 or fewer red cards would be 0.175, and when it comes to the individual probability, selecting exactly 1 red card would be 0.15.

The hypergeometric distribution probabilities or statistics can be derived from the given formula:

Formula:

h(k; N, n, K) = [ KCk ] [ N-KCn-k ] / [ NCn ]

Where;

N is said to be the Population Size

K is said to be the number of Successes in population

n is said to be the Sample Size

k is said to be the number of Successes in Sample

C is said to be combinations

h is said to be hypergeometric

The hypergeometric distribution calculator is an online discrete statistics tool that helps to determine the individual and cumulative hypergeometric probabilities. The hypergeometric calculator will assists you to calculate the following parameters and draw the chart for a hypergeometric distribution:

- probability mass function
- Lower Cumulative Distribution P
- Upper Cumulative Distribution Q
- Mean of hypergeometric distribution
- Variance hypergeometric distribution
- Standard Deviation hypergeometric distribution

This hypergeometric calculator is loaded with user-friendly interface; you just have to follow the given steps to get instant results:

**Inputs:**

- First of all, you have to select the option of Hypergeometric Probability distribution from the distribution from the drop-down menu
- Now, you have to enter the population size (N) into the designated field
- Very next, you have to enter the number of successes in population (K) into the given field
- Now, you have to enter the sample size (n) into the designated field
- Finally, you have to enter number of successes in sample (k) into the designated field of this hypergeometric probability calculator

**Outputs:**

Once done, you have to hit the calculate button, this distribute calculator will shows the following:

- Hypergeometric Probability: P(X = x)
- Cumulative Probability: P(X < x)
- Cumulative Probability: P(X ≤ x)
- Cumulative Probability: P(X > x)
- Cumulative Probability: P(X ≥ x)
- Mean
- Variance
- Standard Deviation
- Hypergeometric Distribution Probability Chart

**Inputs:**

- First of all, you have to choose the option of Hypergeometric Probability distribution (chart) from the drop-down menu
- Very next, you have to select the function for which you want to calculate a table of the probability, it can either be in (probability mass f, lower cumulative distribution P, upper cumulative distribution Q)
- Now, you have to enter the population size (N) into the designated filed of this hypergeometric distribution calculator
- Then, you have to add the number of successes in population (K) into the given box
- Right after, you have to add the sample size (n) into the designated filed of the above calculator
- Then, enter the value of successes in sample (k) initial into the designated field
- Enter the value into the increment field, tell how much you want increment in every repetition for a successes in sample (k) initial
- Now, enter the value to tell how much steps you want to repeat

**Outputs:**

Once done, you have to hit the calculate button, this Hypergeometric distribution (chart) Calculator will shows:

- Table of probability according to the selected function
- Mean
- Variance
- Standard Deviation
- Draws the chart for a hypergeometric distribution

You can use the hypergeometric distribution with populations that are so small, which the outcome of a trial has a large effect on the probability that the next outcome is a non-event or event. For instance, within a population of 10 people, only 7 people have A+ blood. So, try the above distribute calculator to find the hypergeometric distribution.

The hypergeometric experiment has two particularities that are mentioned-below:

- The random selections from the finite population take place without any replacement
- Each item in the population can either be considered as a success or failure

However, a hypergeometric distribution indicates the probability that associated with the occurrence of a specific number of successes in a hypergeometric experiment.

When it comes to hypergeometric experiment, each item in the population can be represented as a success or a failure. The number of successess is said to be a count of the successes in a particular grouping. Therefore, the number of successes in the sample indicates a count of successes in the sample; and the number of successes in the population indicates a count of successes in the population.

A hypergeometric probability is said to be a probability that is associated with a hypergeometric experiment.

Well, the Hypergeometric distribution is to deal with circumstances, which taken into accounts when sample from data set with an acknowledged number of defective items. So, use the above hyper geometric calculator to get ease of hypergeometric distribution calculations!

From Wikipedia, the free encyclopedia – Hypergeometric distribution – Not to be confused with Geometric distribution

From the source of Probability Theory and Mathematical Statistics – Hypergeometric Distribution Example – Lesson 7: Discrete Random Variables

From The source of sanfoundry – Probability and Statistics Questions and Answers about Hypergeometric Distributions