## Variance of Hypergeometric Distribution Solution

STEP 0: Pre-Calculation Summary
Formula Used
Variance of Data = (Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1))
σ2 = (n*NSuccess*(N-NSuccess)*(N-n))/((N^2)*(N-1))
This formula uses 4 Variables
Variables Used
Variance of Data - Variance of Data is the expectation of the squared deviation of the random variable associated with the given statistical data from its population mean or sample mean.
Sample Size - Sample Size is the total number of individuals present in a particular sample drawn from the given population under investigation.
Number of Success - Number of Success is the number of times that a specific outcome which is set as the success of the event occurs in a fixed number of independent Bernoulli trials.
Population Size - Population Size is the total number of individuals present in the given population under investigation.
STEP 1: Convert Input(s) to Base Unit
Sample Size: 65 --> No Conversion Required
Number of Success: 5 --> No Conversion Required
Population Size: 100 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
σ2 = (n*NSuccess*(N-NSuccess)*(N-n))/((N^2)*(N-1)) --> (65*5*(100-5)*(100-65))/((100^2)*(100-1))
Evaluating ... ...
σ2 = 1.0915404040404
STEP 3: Convert Result to Output's Unit
1.0915404040404 --> No Conversion Required
1.0915404040404 1.09154 <-- Variance of Data
(Calculation completed in 00.020 seconds)
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## <Hypergeometric Distribution Calculators

Hypergeometric Distribution
​ Go Hypergeometric Probability Distribution Function = (C(Number of Items in Sample,Number of Successes in Sample)*C(Number of Items in Population-Number of Items in Sample,Number of Successes in Population-Number of Successes in Sample))/(C(Number of Items in Population,Number of Successes in Population))
Standard Deviation of Hypergeometric Distribution
​ Go Standard Deviation in Normal Distribution = sqrt((Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1)))
Variance of Hypergeometric Distribution
​ Go Variance of Data = (Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1))
Mean of Hypergeometric Distribution
​ Go Mean in Normal Distribution = (Sample Size*Number of Success)/(Population Size)

## Variance of Hypergeometric Distribution Formula

Variance of Data = (Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1))
σ2 = (n*NSuccess*(N-NSuccess)*(N-n))/((N^2)*(N-1))

## What is Hypergeometric Distribution?

The Hypergeometric Distribution is a discrete probability distribution that describes the number of successes in a fixed number of Bernoulli trials (i.e. trials with only two possible outcomes: success or failure) without replacement.
The probability mass function (PMF) of the hypergeometric distribution is given by: P(X = x) = (C(K,x) * C(N-K,n-x)) / C(N,n)

The Hypergeometric Distribution is used to model the probability of observing a certain number of "successes" in a fixed number of draws from a finite population, where the probability of success changes on each draw. It is used in many fields such as genetics, quality control, and sampling inspection, in which the sample is drawn without replacement.

## How to Calculate Variance of Hypergeometric Distribution?

Variance of Hypergeometric Distribution calculator uses Variance of Data = (Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1)) to calculate the Variance of Data, Variance of Hypergeometric Distribution formula is defined as the expectation of the squared deviation of the random variable that follows Hypergeometric distribution, from its mean. Variance of Data is denoted by σ2 symbol.

How to calculate Variance of Hypergeometric Distribution using this online calculator? To use this online calculator for Variance of Hypergeometric Distribution, enter Sample Size (n), Number of Success (NSuccess) & Population Size (N) and hit the calculate button. Here is how the Variance of Hypergeometric Distribution calculation can be explained with given input values -> 1.09154 = (65*5*(100-5)*(100-65))/((100^2)*(100-1)).

### FAQ

What is Variance of Hypergeometric Distribution?
Variance of Hypergeometric Distribution formula is defined as the expectation of the squared deviation of the random variable that follows Hypergeometric distribution, from its mean and is represented as σ2 = (n*NSuccess*(N-NSuccess)*(N-n))/((N^2)*(N-1)) or Variance of Data = (Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1)). Sample Size is the total number of individuals present in a particular sample drawn from the given population under investigation, Number of Success is the number of times that a specific outcome which is set as the success of the event occurs in a fixed number of independent Bernoulli trials & Population Size is the total number of individuals present in the given population under investigation.
How to calculate Variance of Hypergeometric Distribution?
Variance of Hypergeometric Distribution formula is defined as the expectation of the squared deviation of the random variable that follows Hypergeometric distribution, from its mean is calculated using Variance of Data = (Sample Size*Number of Success*(Population Size-Number of Success)*(Population Size-Sample Size))/((Population Size^2)*(Population Size-1)). To calculate Variance of Hypergeometric Distribution, you need Sample Size (n), Number of Success (NSuccess) & Population Size (N). With our tool, you need to enter the respective value for Sample Size, Number of Success & Population Size and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
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